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curve #4100

y² = x³ − x² − 56573952540x + 2125201472697600

a-invariants: [0, -1, 0, -56573952540, 2125201472697600]
c-invariants: [2715549721936, -1836157779112394816]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6447990126480
discriminant (Δ): 9637476457740770180597732964000000
Faltings height: 5.2146
naive height: 85.8900
primes of bad reduction: 2, 3, 5, 7, 29, 109, 149, 281
regulator: 1712.1740054883574399295300602114229993463123974242
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:51:34 UTC
last updated: 2026-10-09 14:51:34 UTC

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

(235280, 42880600)
(-1926380/9, 1796712400/27)
(108515445/484, -283992853725/10648)
(392640, -201106080)
(358305, 166896450)
(20877, 30874032)

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 2026-10-09 14:51:34 UTC · history

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