curve #2895

y² + xy = x³ − x² − 337932831634234476430674x + 74246311850890765756949394571864818

a-invariants: [1, -1, 0, -337932831634234476430674, 74246311850890765756949394571864818]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 407739781740207625175610
discriminant (Δ): 88446769142052957460258866900721611612535160889447862321633607172122250
Faltings height: 12.4036
naive height: 174.1450
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 29, 41, 67, 101, 997, 2141, 5711
regulator: 15265377.06014232454133121820671946126920781571633710
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:18 UTC
last updated: 2026-09-26 20:27:18 UTC

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

(23868291739441/64, 4799688346055860717/512)
(405550431229, 62440593046962116)
(377778392347, 22311357692377334)
(394436322937, 48163446052843304)
(89228465644117, 842841517319867492159)
(416690592397, 76047835962924084)
(-3719816798246984583/13476241, 18934924494491225996678129544/49471280711)

Commentary

2-isogenous image of D-z6old678-122, rational kernel x=-185908156668. 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 20:27:18 UTC · history