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curve #1212

y² + xy + y = x³ + x² − 137134090x + 617869049111

a-invariants: [1, 1, 1, -137134090, 617869049111]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 99939775325826
discriminant (Δ): 98519882167161631014912
Faltings height: 3.3830
naive height: 67.8230
primes of bad reduction: 2, 3, 23, 73, 109, 193, 409, 1153
regulator: 20568.66902004134539277725433441163266428746956538921
submitted by: Michael Rubinstein
submitted at: 2026-09-24 13:36:52 UTC
last updated: 2026-09-24 13:36:52 UTC

Witness: 7 independent points log in to add more points →

(-311, 812859)
(6881, 7107)
(7973, 173247)
(8609, 270339)
(54097/9, 2724473/27)
(80041/9, 8493977/27)
(194529/25, 18055823/125)

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 13:36:52 UTC · history

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