curve #1124

y² + xy = x³ − 4401046837403916631215x + 113247068123398333719870687876921

a-invariants: [1, 0, 0, -4401046837403916631215, 113247068123398333719870687876921]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 4836279913743676055658 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
discriminant (Δ): -84687979373575954593160246637280649251977744993986123272608037888 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
Faltings height: 11.2818 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
naive height: 161.1374 ☆ record for ℤ/5ℤ torsion, rank ≥ 7
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 53, 67, 702057860891
regulator: 48424.77000551509256741545227997013265655769471620601
submitted by: dujella
submitted at: 2026-09-23 21:20:10 UTC
last updated: 2026-09-23 21:20:10 UTC

(19668144020, 5856182535325679)
(27196268844, 3697334491928205)
(23690800878, 4720083672205029)
(-71804280804, -7684274698415187)
(-5714779326, -11756333405379435)
(16469438730, 6725429087398149)
(31099970646, 2540611635246813)

found by Eroshkin (2009)

last edited by dujella at 2026-09-23 21:20:11 UTC · history