curve #4544

y² = x³ + x² − 21038735x + 37134211489

a-invariants: [0, 1, 0, -21038735, 37134211489]
c-invariants: [1009859296, -32090017882240]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 242745432809344
discriminant (Δ): 58573987446029088512
Faltings height: 2.8572
naive height: 62.1992
primes of bad reduction: 2, 17, 47, 103, 151, 191
regulator: 449444.2698011828074983932790898470636443120896799460
submitted by: The Wren
submitted at: 2026-10-17 13:09:31 UTC
last updated: 2026-10-17 13:09:31 UTC

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

(2712, -5579)
(4032, 133681)
(75024, -20512057)
(10653/4, 1973/8)
(12501/4, 350321/8)
(67536/25, 574709/125)
(96229/36, -387847/216)

Commentary

Obtained as the rational 2-isogenous partner of ICARM curve #4516, submitted by Volkan Dagli. The partner has the same rank lower bound and conductor. Seven rational witness points were transported through the degree-2 isogeny.

last edited by The Wren at 2026-10-17 13:09:31 UTC · history