curve #1705

y² + xy = x³ − 7352306066465142510x + 7934490853420416757079061636

a-invariants: [1, 0, 0, -7352306066465142510, 7934490853420416757079061636]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 107139953671224474
discriminant (Δ): -1760943923918435865308124881263633473275050585074306121728
Faltings height: 9.7527
naive height: 142.0052
primes of bad reduction: 2, 3, 7, 11, 13, 19, 29, 241, 1181, 113749
regulator: 3651.6396237756694551014987137056786732150889506487
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:13:08 UTC
last updated: 2026-09-25 06:13:08 UTC

(-3122066220, 21383073141066)
(729053052, 54421825375554)
(1187853576, 29615019951426)
(489431670, 66732652145796)
(390665209116/25, 240730923999094074/125)
(3519482694, 160164275470836)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:13:08 UTC · history