curve #2021

y² = x³ − x² − 3032742853505x + 154135201312272321

a-invariants: [0, -1, 0, -3032742853505, 154135201312272321]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 14908677686287650358464 ☆ record for ℤ/2ℤ torsion, rank ≥ 10
discriminant (Δ): 1774936249266666245136723009916565225472
Faltings height: 6.2208
naive height: 97.8351
primes of bad reduction: 2, 3, 7, 17, 23, 31, 41, 127, 4337, 6073, 6673
regulator: 612921212.1520576125704314868849355419799269031615733726895
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:02:08 UTC
last updated: 2026-09-26 05:02:08 UTC

(-8077, 422646588)
(-238657, -929692008)
(-798097, 1437429168)
(1715603, -25941132)
(-1665229, -765953244)
(3082451, -4482606996)
(-670144, -1373154111)
(4080371, 7464264444)
(-1621192, -899928477)
(39983, -181496448)

2-isogenous partner of curve#1382 (NDElkies).

last edited by Steps Unbounded at 2026-09-26 21:40:58 UTC · history