curve #3023

y² = x³ + x² − 265526132483613105674202368780x + 52644732899743733334661578634911125703996100

a-invariants: [0, 1, 0, -265526132483613105674202368780, 52644732899743733334661578634911125703996100]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 28662861085935403583774269180
discriminant (Δ): 849909490292105154064329155897592193270016727909570744403301820138055808582644047968000
Faltings height: 15.6426
naive height: 214.8681
primes of bad reduction: 2, 5, 11, 13, 17, 19, 31, 61, 71, 79, 163, 241, 661, 1129, 99787
regulator: 16531353.2605234007791993764344309609858582214625929165
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:44 UTC
last updated: 2026-09-26 20:33:44 UTC

Witness: 8 independent points log in to add more points →

(24597240001299064/81, -90699937635940342025030/729)
(831611369121431712/1369, -544383732893313377039066102/50653)
(83341752902352120, -24059448296789515209529930)
(49166047684317300/169, 308242719378230664194530/2197)
(891132505099406845/2916, -31634601015903294349928845/157464)
(1089640996179725/4, 5810522996380455405195/8)
(8537431420963546614040/46280809, 992669087871520036795292590848590/314848343627)
(49946708578273738264/189225, 80151436342686309253228984562/82312875)

Commentary

2-isogenous image of D-z6old678-059, rational kernel x=-146458586456760. 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 20:33:44 UTC · history