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curve #1324

y² = x³ + x² − 682000x + 55838851044

a-invariants: [0, 1, 0, -682000, 55838851044]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 22378025224048 ☆ record for ℤ/2ℤ torsion, rank ≥ 7
discriminant (Δ): -1346956853422402953223168
Faltings height: 3.3089
naive height: 63.0146
primes of bad reduction: 2, 13, 17, 103, 127, 149, 191
regulator: 2488.874981879071207204946826428858944004590839943670
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:32:18 UTC
last updated: 2026-09-24 17:32:18 UTC

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

(1864, 247078)
(-8, 236314)
(4074, 347412)
(-3544, 117286)
(11614, 1270672)
(3674/25, 29512132/125)
(-2009/9, 6388226/27)

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 17:32:18 UTC · history

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