Filip Najman

Publications

  1. F. Najman, Compact representation of quadratic integers and integer points on some elliptic curves, Rocky Mountain J. Math. 40 (2010), 1979-2002.
  2. F. Najman, Integer points on two families of elliptic curves, Publ. Math. Debrecen 75 (2009), 401-418.
  3. F. Najman, Torsion of elliptic curves over cyclotomic quadratic fields, Math. J. Okayama Univ. 53 (2011), 75-82.
  4. F. Luca, F. Najman, On the largest prime factor of x2 − 1, Math. Comp. 80 (2011), 429-435. Tables: odd solutions, even solutions
  5. F. Najman, The Diophantine equation x4 ± y4 = iz2 in Gaussian integers, Amer. Math. Monthly 117 (2010), 637-641.
  6. F. Najman, Complete classification of torsion of elliptic curves over quadratic cyclotomic fields, J. Number Theory 130 (2010), 1964-1968
  7. F. Najman, Smooth values of some quadratic polynomials, Glasnik Mat. Ser III 45 (2010), 347-355. Values of x such that the polynomial is smooth: x2 + 1, x2 + 2, x2 + 4, x2 − 2, x2 − 4. (For x2 + 4 and x2 − 4 only the odd values are listed).
  8. F. Najman, Large strings of consecutive smooth integers, Arch. Math. (Basel) 97 (2011), 319-324.
  9. S. Kamienny, F. Najman, Torsion groups of elliptic curves over quadratic fields, Acta. Arith. 152 (2012), 291-305. Errata
  10. F. Najman, Torsion of elliptic curves over cubic fields, J. Number Theory, 132 (2012), 26-36.
  11. A. Dujella, F. Najman, Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization, Period. Math. Hungar. 65 (2012), 193-203., special issue with papers from the “11th Central European Conference on Cryptography”.
  12. F. Najman, Exceptional elliptic curves over quartic fields, Int. J. Number Theory, 8 (2012), 1231-1246.
  13. F. Najman, On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree, Glasgow Math. J. 57 (2015), 465-473.
  14. J. Bosman, P. Bruin, A. Dujella, F. Najman, Ranks of elliptic curves with prescribed torsion over number fields, Int. Math. Res. Not. IMRN 2014 (2014), 2885-2923.
  15. F. Najman, Some rank records for elliptic curves with prescribed torsion over quadratic fields, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat 22 (2014). 215-220., special issue with papers from the „Workshop on Algebraic and Analytic Number Theory and their Applications“
  16. A. Dujella, F. Najman, N. Saradha, T. N. Shorey, Products of three factorials, Publ. Math. Debrecen 85 (2014) 123-130.
  17. P. Bruin, F. Najman, The growth of the rank of Abelian varieties upon extensions, Ramanujan J. 39 (2016), 259-269.
  18. F. Najman, Torsion of rational elliptic curves over cubic fields and sporadic points on X1(n), Math. Res. Letters 23 (2016) 245-272.
  19. F. Najman, The number of twists with large torsion of an elliptic curve, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109 (2015), 535-547.
  20. P. Bruin, F. Najman, Hyperelliptic modular curves X0(n) and isogenies of elliptic curves over quadratic fields, LMS J. Comput. Math. 18 (2015) 578-602. Errata
  21. M. Mikić, F. Najman, On the number of n-isogenies of elliptic curves, Glasnik Mat. Ser III, 50 (2015) 333-348.
  22. E. Gonzalez-Jimenez, F. Najman, J. M. Tornero, Torsion of rational elliptic curves over cubic fields, Rocky Mountain J. Math. 46 (2016), 1899-1917.
  23. P. Bruin, F. Najman, A criterion to rule out torsion groups for elliptic curves over number fields, Res. Number Theory 2 (2016), 1-12. Errata
  24. F. Najman, Isogenies of non-CM elliptic curves with rational j-invariants over number fields, Math. Proc. Cambridge Philos. Soc. 164 (2018), 179-184.
  25. H. B. Daniels, A. Lozano-Robledo, F. Najman, A. V. Sutherland, Torsion points on rational elliptic curves over the compositum of all cubic fields, Math. Comp. 87 (2018), 425-458.
  26. F. Najman, Tamagawa Numbers of elliptic curves with C13 torsion over quadratic fields, Proc. Amer. Math. Soc. 145 (2017), 3747 -3753.
  27. P. Bruin, F. Najman, Fields of definition of elliptic curves with prescribed torsion, Acta Arith. 181 (2017), 85-96.
  28. E. Gonzalez-Jimenez, F. Najman, Growth of torsion groups of elliptic curves upon base change, Math. Comp. 89 (2020), 1457-1485. Errata
  29. M. Derickx, F. Najman, Torsion of elliptic curves over cyclic cubic fields, Math. Comp. 88 (2019), 2443-2459.
  30. S. Le Fourn, F. Najman, Torsion of ℚ-curves over quadratic fields, Math. Res. Letters 27 (2020), 209-225.
  31. M. Chou, H. Daniels, I. Krijan, F. Najman, Torsion of elliptic curves over ℤp extensions of ℚ, New York J. Math. 27 (2021), 99-123.
  32. M. Derickx, F. Najman, S. Siksek, Elliptic curves over totally real cubic fields are modular, Algebra & Number Theory, 14 (2020), 1791-1800.
  33. E. Gonzalez-Jimenez, F. Najman, An algorithm for determining torsion growth of elliptic curves, Exp. Math. 32 (2023), 70-81.
  34. F. Najman, G. Turcas, Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields, Int. J. Number Theory 17 (2021), 1729-1738.
  35. J. E. Cremona, F. Najman, ℚ-curves over odd degree number fields, Res. Number Theory, 7, 62 (2021).
  36. P. Bruin, F. Najman, Counting elliptic curves with prescribed level structures over number fields, J. London Math. Soc. 102 (2022), 2415-2435.
  37. F. Najman, A. Trbović, Splitting of primes in number fields generated by points on some modular curves, Res. Number Theory, 8, 28 (2022).
  38. A. Bourdon, F. Najman, Sporadic points of odd degree on X1(n) coming from ℚ-curves, Algebra & Number Theory, to appear. code
  39. F. Najman, B. Vukorepa, Quadratic points on bielliptic modular curves, Math. Comp. 92 (2023), 1791-1816.
  40. F. Najman, On r-isogenies over ℚ(ζr) of elliptic curves with rational j-invariants, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 118 (2024), 134.
  41. B. S. Banwait, F. Najman, O. Padurariu, Cyclic isogenies of elliptic curves over a fixed quadratic field, Math. Comp. 93 (2024), 841-862.
  42. N. Freitas, F. Najman, Two results on xr + yr = dzp, Proc. Amer. Math. Soc. 152 (2024), 591-598.
  43. F. Najman, P. Orlić, Gonality of the modular curve X0(N), Math. Comp. 93 (2024), 863-886. Errata
  44. N. Adžaga, T. Keller, P. Michaud-Jacobs, F. Najman, E. Ozman, B. Vukorepa, Computing quadratic points on modular curves X0(N), Math. Comp. 93 (2024), 1371-1397.
  45. M. Derickx, F. Najman, Hyperelliptic and trigonal modular curves in characteristic p, Q. J. Math (Oxford) 76 (2025), 1-18. Errata
  46. P. Michaud-Jacobs, F. Najman, Quadratic points on X0(163), J. Algebra, 666 (2025), 279-288.
  47. A. Bourdon, S. Hashimoto, T. Keller, Z. Klagsbrun, D. Lowry-Duda, T. Morrison, F. Najman, H. Shukla, Towards a Classification of Isolated j-invariants, With an appendix by Maarten Derickx and Mark van Hoeij, Math. Comp. 94 (2025), 447-473. Errata
  48. M. Derickx, F. Najman, Classification of torsion of elliptic curves over quartic fields, J. Reine Angew. Math. 829 (2025), 123-156. Errata
  49. F. Najman, I. Novak, Quadratic points on modular curves X0(N) for N ≤ 100, Res. Number Theory, 12, (2026), 23. Errata
  50. M. Derickx, F. Najman, Sporadic points on X0(N), preprint.
  51. F. Najman, M. Varivoda, Torsion groups of elliptic curves that appear infinitely often over septic, octic and nonic fields, preprint.
  52. M. Derickx, S. Hashimoto, F. Najman, A. Shnidman, Rational points on modular curves: parameterization and geometric explanations, preprint.
  53. J. S. Balakrishnan, F. Najman, A. Shnidman, A. V. Sutherland, Rational torsion on simple genus two Jacobians, preprint.
  54. F. Najman, Classification of torsion of elliptic curves over quintic fields, preprint.
  55. F. Najman, Classification of torsion of elliptic curves over sextic fields*, preprint.
  56. F. Najman, Torsion of elliptic curves over number fields of degree 6, 7, 8 and 9**, preprint.

* The mathematics in this paper is primarily AI-generated, but I carefully checked and rewrote it.
** The mathematics in this paper is primarily AI-generated, and I have not yet fully checked it.