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curve #4102

y² = x³ − x² − 202314573841x + 378928629586705

a-invariants: [0, -1, 0, -202314573841, 378928629586705]
c-invariants: [9711099544384, -327336069365646848]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 72795633914304960
discriminant (Δ): 529920431698550647243291988060160000
Faltings height: 5.5443
naive height: 89.7129
primes of bad reduction: 2, 3, 5, 23, 31, 41, 73, 79, 223, 2017
regulator: 21961.45647088260564827104331927128809425006391716534
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:52:12 UTC
last updated: 2026-10-09 14:52:12 UTC

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

(-47327, 99236400)
(-105077, 143099100)
(2675623, 4314363000)
(-8295, 45349280)
(549705, 235101520)
(3147601, 5527031808)
(462557553/361, 9316147838000/6859)

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 14:52:12 UTC · history

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