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curve #1306

y² = x³ − x² − 3304393108x + 72733213658212

a-invariants: [0, -1, 0, -3304393108, 72733213658212]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 15460567128600
discriminant (Δ): 23902913593794684893796000000
Faltings height: 4.2848
naive height: 77.3692
primes of bad reduction: 2, 3, 5, 11, 19, 71, 89, 109, 179
regulator: 707.36103080451997832486219361396857798643608814092
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:29:14 UTC
last updated: 2026-09-24 17:29:14 UTC

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

(37212, 1139050)
(35692, 510150)
(50728, 5970366)
(456528/49, 2242789450/343)
(456862, 306464400)
(157684/25, 902618598/125)

Commentary

Torsion Z/2+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 17:29:15 UTC · history

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