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curve #4104

y² = x³ − x² − 137134957001x + 4574483689718985

a-invariants: [0, -1, 0, -137134957001, 4574483689718985]
c-invariants: [6582477936064, -3952314413049586688]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 394985569602442560
discriminant (Δ): 156013600194165996065770318099353600
Faltings height: 5.4437
naive height: 88.5463
primes of bad reduction: 2, 3, 5, 7, 19, 29, 37, 59, 67, 73, 97, 103
regulator: 7158.413639276988629621630542512764511155058537546629
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:52:33 UTC
last updated: 2026-10-09 14:52:33 UTC

Witness: 7 independent points log in to add more points →

(-118657, 138476940)
(373523, 73925640)
(-41050297/121, -146114027460/1331)
(668888, 460558425)
(4891201, 10786572272)
(27263, 29258100)
(-378952, 46072215)

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 14:52:33 UTC · history

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