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curve #1408

y² + xy + y = x³ − x² − 405703697389776392x + 99463223712366882392777291

a-invariants: [1, -1, 1, -405703697389776392, 99463223712366882392777291]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 401170770
discriminant (Δ): -19062232464005432782129313148502199614036612608000
Faltings height: 8.6928
naive height: 133.2468
primes of bad reduction: 2, 3, 5, 7, 11, 13, 61, 73
regulator: 52.4182291758370471607476286759590104278278
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:23:18 UTC
last updated: 2026-09-24 23:23:18 UTC

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

(367020351, 28044434569)
(37539753952892169/101143249, 116250290181239654949757/1017197655193)

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 23:23:19 UTC · history

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