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curve #1283

y² = x³ + x² − 32721460x + 51427415900

a-invariants: [0, 1, 0, -32721460, 51427415900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 69894829680
discriminant (Δ): 1099189623599147003040000
Faltings height: 3.3198
naive height: 63.5242
primes of bad reduction: 2, 3, 5, 13, 61, 181, 2029
regulator: 406.495024876651991501355820582416877003179199071
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:25:19 UTC
last updated: 2026-09-24 17:25:19 UTC

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

(-2482, 342576)
(-16675/4, 2717715/8)
(9230, 732000)
(64130, 16177200)
(39950, 7906080)

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 2026-09-24 17:25:19 UTC · history

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