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curve #1338

y² = x³ + x² − 180273846630x + 29574795822924753

a-invariants: [0, 1, 0, -180273846630, 29574795822924753]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 30827533076473380
discriminant (Δ): -2904210058492286706861070251750000
Faltings height: 5.2730
naive height: 89.3745
primes of bad reduction: 2, 3, 5, 13, 19, 23, 31, 251, 11623243
regulator: 3317.806601735595242444481719597011548418886214527662
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:34:42 UTC
last updated: 2026-09-24 17:34:42 UTC

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

(259626, -16472625)
(-375099, -210758925)
(-489954, 16883685)
(273276, -26805675)
(282597, 34619715)
(236226, 13097175)
(370629/4, -935234625/8)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:34:42 UTC · history

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