curve #1632

y² + xy = x³ − 6582967677923856303475737305x + 359032669729548252202280621897667116372025

a-invariants: [1, 0, 0, -6582967677923856303475737305, 359032669729548252202280621897667116372025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/7ℤ
conductor (N): 9839692872536169822270
discriminant (Δ): -37429064694956097356266175978815006278562024211322773990674372018934784112559070000000
Faltings height: 15.1139
naive height: 204.8916
primes of bad reduction: 2, 3, 5, 7, 13, 199, 541, 941, 5082541003
regulator: 470999.5712833991032633899245384203168086548213
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:57:19 UTC
last updated: 2026-09-25 01:57:19 UTC

(104798746251842024260/4206601, 3958373849776665843538030489745/8627738651)
(-696684585583435200927557630/7702118022361, 9897711369171457389475237029485316346415/21375449381799790109)
(196538669050538471958423243790/301859455054609, 86508795101790563741277234171715613274420365/5244537263642647390727)
(99047383022224548938537606290889410/407242274254935090409, 29796068597852254090830580087695581650323330107956055/8218248727508713417088293833077)

Torsion Z/7. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:57:19 UTC · history