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curve #1708

y² + xy + y = x³ − x² − 3266038616x + 1807214804798370

a-invariants: [1, -1, 1, -3266038616, 1807214804798370]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 104067785215251
discriminant (Δ): -1408691989476819092254743109782063
Faltings height: 5.0398
naive height: 83.7843
primes of bad reduction: 3, 11, 13, 199, 367, 433, 2557
regulator: 14370.391947962429895538577753714591661360141013778
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:13:38 UTC
last updated: 2026-09-25 06:13:38 UTC

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

(-118849/4, -346570641/8)
(14010651/4, -52451120391/8)
(-121177, 20642760)
(-4788039/64, 20708159239/512)
(23534886/25, 114028604694/125)
(48371, 41956854)

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 06:13:38 UTC · history

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