curve #2910

y² + xy + y = x³ + x² − 5210802873593686717261920x + 4559195450326040291819893761582786945

a-invariants: [1, 1, 1, -5210802873593686717261920, 4559195450326040291819893761582786945]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 548088118837830139058490
discriminant (Δ): 75447976164590962961620349524966179459183076488903823196160000000000000000
Faltings height: 13.0245
naive height: 182.3519
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 47, 59, 61, 349, 21269
regulator: 1965606.217744365299818339264942494843646289636127023
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:59 UTC
last updated: 2026-09-26 20:27:59 UTC

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

(10199403067316397/6889, 171276056690467005708631/571787)
(536262284932253/361, 2131845669143276528967/6859)
(1394958071573, 69310365770964213)
(4598358387048557/2809, 96013258617980079138801/148877)
(194903562814587/169, 635276519251051813461/2197)
(63001708882803053/32761, 7617699475306313103358833/5929741)
(54038049619101077/37249, 1654313818251871148581941/7189057)

Commentary

2-isogenous image of D-z2z4old678-067, rational kernel x=-11094864572589/4. Source: https://dujella.github.io/tors/z2z4old678.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 20:27:59 UTC · history