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curve #1700

y² + xy = x³ − x² − 6464860713x + 199495637654769

a-invariants: [1, -1, 0, -6464860713, 199495637654769]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 37109896434
discriminant (Δ): 99810817853925065393787240492
Faltings height: 4.4289
naive height: 79.3825
primes of bad reduction: 2, 3, 13, 23, 107, 4957
regulator: 481.068396285720901972146198793557614920159140775
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:12:18 UTC
last updated: 2026-09-25 06:12:18 UTC

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

(1027159/25, 222230917/125)
(59433, 4990344)
(14552412/289, -6408496401/4913)
(-18606, -17692095)
(-41997, -19902027)

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 06:12:18 UTC · history

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