curve #3975

y² + xy + y = x³ + 52506820321303x + 10779070569158888762780

a-invariants: [1, 0, 1, 52506820321303, 10779070569158888762780]
c-invariants: [-2520327375422567, -9313116967972788827908285]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 2485766715136584389804778
discriminant (Δ): -50202637097712729945905710319823807028905421296
Faltings height: 7.6400
naive height: 114.9869
primes of bad reduction: 2, 3, 11, 23, 71, 73, 227, 277, 317, 383, 467, 3853
regulator: 1000672039810.884987248718042594325489366937393217201135918
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:37:47 UTC
last updated: 2026-10-05 04:37:47 UTC

Witness: 10 independent points log in to add more points →

(-158878540404/10201, 81024275441379344/1030301)
(8350092, 108622292656)
(-171783911997/9409, 55783338932291998/912673)
(-29593413744309/1792921, 176691167568066682426/2400721219)
(-2386376877393/1990921, 290782142420580932386/2809189531)
(-34724937645396/11526025, 4027598374058541065552/39130854875)
(1749567969/64, 92498955002933/512)
(126986215527/1681, 46016511969168626/68921)
(712457633619/47089, 1252949062533057742/10218313)
(655368848383002489/191545600, 530549624415289695413093707/2650991104000)

Commentary

Unlisted rational-isogeny neighbor of curve#3617 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:37:47 UTC · history