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curve #1673

y² + xy + y = x³ − 7503915729393x + 7309951276097945008

a-invariants: [1, 0, 1, -7503915729393, 7309951276097945008]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 57274747140390
discriminant (Δ): 3958220542619781996487653157593784618500
Faltings height: 6.3396
naive height: 100.5529
primes of bad reduction: 2, 3, 5, 13, 19, 43, 61, 149, 19777
regulator: 1518.41525648362062602881265921401609623793620682
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:58:19 UTC
last updated: 2026-09-25 02:58:19 UTC

Witness: 5 independent points log in to add more points →

(-2008996, 3779476500)
(1184024, 291013455)
(5984114, 13289657175)
(-438311698/289, 19159465210359/4913)
(-150786739/49, 385670174700/343)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:58:19 UTC · history

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