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curve #3453

y² = x³ − 97351728669x + 3227101284680901

a-invariants: [0, 0, 0, -97351728669, 3227101284680901]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 18292854230884044
discriminant (Δ): 54549859578690223898381758910889744
Faltings height: 5.3566
naive height: 87.5184
primes of bad reduction: 2, 3, 7, 17, 19, 29, 53, 560227
regulator: 5554.969579546928969014904601221197214125921886135657
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:37:31 UTC
last updated: 2026-09-27 05:37:31 UTC

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

(-224135, 117419221)
(-107532, 111589071)
(40977/4, 377857617/8)
(-306443, 65441719)
(941895, 864378039)
(349855, 109498159)
(-141243, 118994169)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:37:31 UTC · history

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