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curve #4098

y² = x³ + x² − 349223105919x + 58203316744233457

a-invariants: [0, 1, 0, -349223105919, 58203316744233457]
c-invariants: [16762709084128, -50287766243272211584]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 5113284222183888540933248
discriminant (Δ): 1262307660291060760412209721138853632
Faltings height: 5.6354
naive height: 91.3505
primes of bad reduction: 2, 7, 23, 103, 137, 193, 367, 1327, 2417, 11057
regulator: 29281214.42293003304189675174283075479514434174229375129221
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:51:12 UTC
last updated: 2026-10-09 14:51:12 UTC

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(651192, -327003181)
(-451417, 351937816)
(-119831, -313576746)
(489893/4, -1051320073/8)
(25679, -221929156)
(680528, -368392031)
(-454457/9, -7429106132/27)
(-2526523/4, 1309412167/8)
(-1602968/9, 9146292967/27)
(1157624, 1097843251)

Commentary

Torsion 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 14:51:12 UTC · history

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