curve #3351

y² + xy + y = x³ − 117507131851023x + 490276827592505578756

a-invariants: [1, 0, 1, -117507131851023, 490276827592505578756]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 57274747140390
discriminant (Δ): 1471274953921175179720304178694125843750
Faltings height: 6.6861
naive height: 108.8062
primes of bad reduction: 2, 3, 5, 13, 19, 43, 61, 149, 19777
regulator: 48589.2882074758600329220050948485150796139586163
submitted by: David Renshaw
submitted at: 2026-09-26 21:10:14 UTC
last updated: 2026-09-26 21:10:14 UTC

Witness: 5 independent points log in to add more points →

(17511370, -61672310698)
(6276670, -55286473)
(8396420, 9772515027)
(87198258296/7225, -17697021500106849/614125)
(18190377830/49, -2452396608802239/343)

Commentary

Rationally isogenous to curve#1673 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-26 21:10:14 UTC · history