curve #1618

y² + xy = x³ − 2787944203818377510058020x + 1414181100211611864227540687565296400

a-invariants: [1, 0, 0, -2787944203818377510058020, 1414181100211611864227540687565296400]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3845501537362524390
discriminant (Δ): 522898339387370986301562653628353200877869247782082620839127000878144000000
Faltings height: 13.0509
naive height: 180.4756
primes of bad reduction: 2, 3, 5, 13, 23, 29, 31, 73, 661, 2459, 4019
regulator: 15606.13015871309311576292879646409757738723748
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:41:11 UTC
last updated: 2026-09-25 01:41:11 UTC

(55817343460087019140/102596641, 251220678791542174322074115020/1039201376689)
(-61375901179027160/52441, 21055025668546338264613420/12008989)
(106152431881266772360/200873929, 846759912370808066339751072460/2846986195717)
(5086679025623293600/3690241, 3092114781710484847366157380/7088952961)

Torsion Z/6+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:41:11 UTC · history