curve #4545

y² = x³ + x² + 41585x + 12874449

a-invariants: [0, 1, 0, 41585, 12874449]
c-invariants: [-1996064, -11111547520]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 562446302336
discriminant (Δ): -76052864109269248
Faltings height: 1.9204
naive height: 46.2625
primes of bad reduction: 2, 17, 41, 97, 103, 631
regulator: 55893.018314688265068163835902307500142202630999206
submitted by: The Wren
submitted at: 2026-10-17 13:11:06 UTC
last updated: 2026-10-17 13:11:06 UTC

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

(-176, 367)
(352, 8441)
(-2651/36, 662887/216)
(133/4, 30247/8)
(2773/4, 154993/8)
(7369/16, 729523/64)

Commentary

Obtained as the rational 2-isogenous partner of ICARM curve #4521, 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 13:11:06 UTC · history