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curve #1235

y² + xy + y = x³ − 1058403x + 112021162

a-invariants: [1, 0, 1, -1058403, 112021162]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 121340359518
discriminant (Δ): 70451321058994637412
Faltings height: 2.4996
naive height: 53.2304
primes of bad reduction: 2, 3, 7, 43, 193, 337, 1033
regulator: 165.43016097091658107232346492438278025683828076888
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:37:11 UTC
last updated: 2026-09-24 14:37:11 UTC

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

(-1054, 8073)
(-796, 21618)
(-667, 23166)
(1913, 70380)
(2816, 138105)
(5525, 400878)

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 14:37:11 UTC · history

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