curve #4543

y² = x³ − x² − 63247380x − 59393074314

a-invariants: [0, -1, 0, -63247380, -59393074314]
c-invariants: [3035874256, 51333831452800]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 143073212630034624
discriminant (Δ): 14667286741539635902356672
Faltings height: 3.5207
naive height: 65.5013
primes of bad reduction: 2, 3, 7, 19, 31, 41, 43, 1033, 99241
regulator: 3781219.54543993478228174183762506637737663760118778946
submitted by: The Wren
submitted at: 2026-10-17 13:07:32 UTC
last updated: 2026-10-17 13:07:32 UTC

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

(-5497, 349492)
(-5129, 360624)
(-1957, 238502)
(20791, -2759064)
(40091, -7863914)
(54071, -12433976)
(-3811/4, 2737/8)
(42629/4, -5524453/8)

Commentary

Obtained as the rational 2-isogenous partner of ICARM curve #4505, submitted by Volkan Dagli. The partner has the same rank lower bound and conductor. Eight rational witness points were transported through the degree-2 isogeny.

last edited by The Wren at 2026-10-17 13:07:32 UTC · history