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curve #1649

y² + xy + y = x³ + x² − 1115268625x + 11522290672367

a-invariants: [1, 1, 1, -1115268625, 11522290672367]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 274613993610
discriminant (Δ): 31422351001431807466536960000
Faltings height: 4.1836
naive height: 74.1107
primes of bad reduction: 2, 3, 5, 11, 17, 89, 550009
regulator: 134.052509624604140500266685617992810335468836016
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:24:20 UTC
last updated: 2026-09-25 02:24:20 UTC

Witness: 5 independent points log in to add more points →

(95825, -28058082)
(455, 3318648)
(296563/9, 87263752/27)
(-15253, 5006136)
(-37319, -1063136)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:24:20 UTC · history

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