curve #793

y² + y = x³ + x² − 4070928502x + 78946908330992

a-invariants: [0, 1, 1, -4070928502, 78946908330992]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 85536680945963752284246181031
discriminant (Δ): 1625196937973311293400677439589
Faltings height: 4.5107
naive height: 77.9950
primes of bad reduction: 19, 4501930576103355383381377949
regulator: 1203461842.698767097858697705579271132402842760559181246982097572
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:41:04 UTC
last updated: 2026-09-18 12:41:04 UTC

(20568, 1979296)
(67156, -10413112)
(51367, 2318085)
(-77651/4, -98194721/8)
(49885, 103008)
(82405/4, -15645117/8)
(89063, 20563386)
(50276, -1166569)
(-43310, -13191729)
(428, 8786616)
(203671, -87741174)
(49961, -519109)
(-21859, 12549471)

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

last edited by Michael Rubinstein at 2026-09-18 12:41:04 UTC · history