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curve #1365

y² = x³ + x² − 53518757176x + 1758039920673780

a-invariants: [0, 1, 0, -53518757176, 1758039920673780]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1320567443182219149040
discriminant (Δ): 8475444276013003362329623897425920
Faltings height: 5.2030
naive height: 85.7235
primes of bad reduction: 2, 5, 29, 71, 89, 229, 401, 557, 631, 2791
regulator: 2573472.0961797332058169021971462846687847751977722471945
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:39:22 UTC
last updated: 2026-09-24 17:39:22 UTC

Witness: 9 independent points log in to add more points →

(-219476, -54148634)
(-11246, -48564284)
(-80329, 74423194)
(840154, -741501716)
(5084, 38549734)
(-34214, -59574164)
(10911594/25, -31010544228/125)
(212759, 1523234)
(8436, 36154614)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:39:22 UTC · history

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