curve #2894

y² + xy = x³ − 99798749773876104861630x + 5038970689071293013254867611320900

a-invariants: [1, 0, 0, -99798749773876104861630, 5038970689071293013254867611320900]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 75879741797208175256430
discriminant (Δ): 52645367214393440293642741803951273012786168069023227914816000000000000
Faltings height: 12.2640
naive height: 170.4859
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 67, 79, 233, 5828761
regulator: 28787.27382925798132094949688444203275046535872375966
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:14 UTC
last updated: 2026-09-26 20:27:14 UTC

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

(1320820240222140/1369, 45498789255481341288810/50653)
(-27492815280, 88101879236616210)
(49716526449660, -350543920216810114830)
(-233985590340, 124819598526685170)
(175897573867260/361, -1841638066801206818970/6859)
(-255177298020, 117853258806596850)
(-1225188845380170384406140/4023157419961, 684169701653772957284959125872315370/8069572712966794541)

Commentary

2-isogenous image of D-z6old678-149, rational kernel x=-415131437281/4. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by 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 20:27:14 UTC · history