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curve #4103

y² = x³ − x² − 265931758808x + 3204586620170112

a-invariants: [0, -1, 0, -265931758808, 3204586620170112]
c-invariants: [12764724422800, -2768686251480440000]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 109507405690597200
discriminant (Δ): 1199187190108504002145649264784000000
Faltings height: 5.6124
naive height: 90.5331
primes of bad reduction: 2, 3, 5, 11, 13, 29, 31, 47, 73, 313, 661
regulator: 8613.278476488322405837470029741672598748836131513074
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:52:22 UTC
last updated: 2026-10-09 14:52:22 UTC

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

(-199208, 219715600)
(-388618, -218768550)
(566492, 185339700)
(-40868, 118340300)
(-25684, 100089132)
(-432948, -192835500)
(-519748, -31908300)

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 14:52:22 UTC · history

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