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curve #1329

y² = x³ + x² − 186847905x + 1879275186559

a-invariants: [0, 1, 0, -186847905, 1879275186559]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 42717604222528
discriminant (Δ): -1108296176144565022199676928
Faltings height: 3.8809
naive height: 70.0470
primes of bad reduction: 2, 17, 47, 89, 263, 401
regulator: 3801.527734610534947761661799561021911383797466441773
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:33:10 UTC
last updated: 2026-09-24 17:33:10 UTC

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

(-3573, 1581544)
(10061, 1008916)
(-7381, 1690072)
(-10390, 1642897)
(11115, 1084328)
(214571, 99200984)
(11387, 1108264)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:33:10 UTC · history

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