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curve #1311

y² = x³ + x² − 4349666225x + 44814999639375

a-invariants: [0, 1, 0, -4349666225, 44814999639375]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 23304567817920
discriminant (Δ): 4399133337558263657212323840000
Faltings height: 4.5735
naive height: 78.1937
primes of bad reduction: 2, 3, 5, 23, 41, 43, 59, 73, 139
regulator: 669.23701190127891002340630698637094921013220637156
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:30:05 UTC
last updated: 2026-09-24 17:30:05 UTC

Witness: 6 independent points log in to add more points →

(144895, -49564080)
(-61622, 8880231)
(-56585, -10476960)
(-28985, -12105360)
(60799, 2260080)
(10210, 1212165)

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 2026-09-24 17:30:05 UTC · history

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