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curve #1518

y² = x³ + x² − 76017x + 8041744

a-invariants: [0, 1, 0, -76017, 8041744]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 250604
discriminant (Δ): 68644445264
Faltings height: 1.3513
naive height: 45.3298
primes of bad reduction: 2, 31, 43, 47
regulator: 5.9118287035192999878412358737383353695524725
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:48:40 UTC
last updated: 2026-09-25 00:48:40 UTC

Witness: 3 independent points log in to add more points →

(-309, 1457)
(208, 1128)
(1148, 37882)

Commentary

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

last edited by Michael Rubinstein at 2026-09-25 00:48:40 UTC · history

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