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curve #1403

y² + xy + y = x³ − 240339832968932054x + 45350987272091625246362156

a-invariants: [1, 0, 1, -240339832968932054, 45350987272091625246362156]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 103273170
discriminant (Δ): 1380532103329034552579271510469092301056300
Faltings height: 8.2815
naive height: 131.6761
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 181
regulator: 197.765026399407158291215763108282861595989
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:21:54 UTC
last updated: 2026-09-24 23:21:54 UTC

Witness: 2 independent points log in to add more points →

(207880745981397/734449, -86648777362697401/629422793)
(296330489616991983/98029801, 159308329847298459365523043/970593059701)

Commentary

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:21:55 UTC · history

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