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curve #1727

y² = x³ − 3367335996300x + 30300093061294898000

a-invariants: [0, 0, 0, -3367335996300, 30300093061294898000]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 1219827152174400
discriminant (Δ): -394173664417349484357751912072696320000000
Faltings height: 6.6610
naive height: 103.2385
primes of bad reduction: 2, 3, 5, 7, 11, 17, 47, 53, 83, 313
regulator: 4912.0999087865319104608870772585696536332879182045
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:16:47 UTC
last updated: 2026-09-25 06:16:47 UTC

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

(43849585/4, -289637839575/8)
(3294640, 7414047900)
(-11856695/4, -30185840475/8)
(-588555566/361, -38469453441048/6859)
(2940965, -6770087975)
(-73305614/25, -483521990616/125)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:16:47 UTC · history

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