curve #2900

y² + xy = x³ − 31078308360572257316407940x + 67044298039643204207014551829281411600

a-invariants: [1, 0, 0, -31078308360572257316407940, 67044298039643204207014551829281411600]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 64632587449756916613210
discriminant (Δ): -20703810830352605864713118675636387316811184727697044587406245318457024000000
Faltings height: 13.4818
naive height: 187.7200
primes of bad reduction: 2, 3, 5, 11, 19, 29, 97, 127, 991, 1709, 2437, 6991
regulator: 6020328.201165816538957533048615424275978819401721657
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:30 UTC
last updated: 2026-09-26 20:27:30 UTC

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

(59299434396520/9, 328816225701576338420/27)
(7669368204880, 16727203845809375860)
(-21694499997105/4, 69770671431563702205/8)
(345151154320774/169, -7639502525555992978886/2197)
(7586519153980, 16368022858044209260)
(-16104440589728120/7921, 7781095831706503931326940/704969)
(23993024579410, -114600760937374920890)

Commentary

2-isogenous to curve#1120 via the rational 2-torsion point x=3220528153480. 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 20:27:30 UTC · history