curve #4546

y² = x³ + x² + 83121x + 13940161

a-invariants: [0, 1, 0, 83121, 13940161]
c-invariants: [-3989792, -12020360320]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 865016887424
discriminant (Δ): -120370559952599296
Faltings height: 1.9621
naive height: 46.4197
primes of bad reduction: 2, 23, 41, 103, 1697
regulator: 44258.738207372344063317914714116684852879656253271
submitted by: The Wren
submitted at: 2026-10-17 13:13:23 UTC
last updated: 2026-10-17 13:13:23 UTC

Witness: 6 independent points log in to add more points →

(488, 13075)
(1232, 44585)
(-259/4, 23035/8)
(833/16, -274615/64)
(2477/4, 139315/8)
(3941/4, 259625/8)

Commentary

Obtained as the rational 2-isogenous partner of ICARM curve #4522, submitted by Volkan Dagli. The partner has the same rank lower bound and conductor. Six rational witness points were transported through the degree-2 isogeny.

last edited by The Wren at 2026-10-17 13:13:23 UTC · history