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curve #1720

y² = x³ + x² − 53267504x + 86611984356

a-invariants: [0, 1, 0, -53267504, 86611984356]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 125565648
discriminant (Δ): 6431094447639502479381504
Faltings height: 3.4593
naive height: 64.9861
primes of bad reduction: 2, 3, 13, 23, 673
regulator: 39.57951515727403217911097772794856564678551279
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:15:37 UTC
last updated: 2026-09-25 06:15:37 UTC

Witness: 4 independent points log in to add more points →

(68176, 17701398)
(-6353, 410670)
(-7874, 133848)
(-7406, 273780)

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 06:15:38 UTC · history

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