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curve #1297

y² = x³ − 10972227x + 13769230210

a-invariants: [0, 0, 0, -10972227, 13769230210]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 138417695568
discriminant (Δ): 2636790713228922458112
Faltings height: 2.9057
naive height: 60.2462
primes of bad reduction: 2, 3, 19, 43, 71, 73, 227
regulator: 244.70918997284217677420076965011915140599988490238
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:27:43 UTC
last updated: 2026-09-24 17:27:43 UTC

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

(743, 77634)
(1679, 8946)
(2111, 3762)
(2786, 69462)
(3921, 176152)
(2318, 28116)

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 17:27:43 UTC · history

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