curve #2938

y² = x³ − x² − 50331506738970x + 127925541568059206400

a-invariants: [0, -1, 0, -50331506738970, 127925541568059206400]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 248416958159611680
discriminant (Δ): 1090526541027896072952265581104372960040000
Faltings height: 6.8107
naive height: 106.2626
primes of bad reduction: 2, 3, 5, 17, 19, 31, 59, 67, 659, 19841
regulator: 33083.55048248698146177904295214569044456546866031076
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:13 UTC
last updated: 2026-09-26 20:29:13 UTC

Witness: 7 independent points log in to add more points →

(31470685/4, -118374201375/8)
(6871800, -10322551980)
(-746240, -12847932240)
(1104406005/4, -36690281354205/8)
(8136760, 16034320740)
(2171040025/64, -99090715145565/512)
(5507040, -4214568600)

Commentary

2-isogenous to curve#2101 via the rational 2-torsion point x=16256659. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:29:13 UTC · history