curve #2848

y² + xy = x³ − 176437766116755715593028421000x + 28525101373243316234591662405070447436360000

a-invariants: [1, 0, 0, -176437766116755715593028421000, 28525101373243316234591662405070447436360000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 286506236810100584130
discriminant (Δ): 13343531912768895289323777036487063158707882858277501774785059103095699266678284640000
Faltings height: 15.4496
naive height: 213.6419
primes of bad reduction: 2, 3, 5, 7, 19, 31, 41, 347, 3001, 4049, 13399
regulator: 674378.759178133690327059763816189870983279655587
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:11 UTC
last updated: 2026-09-26 20:25:11 UTC

Witness: 5 independent points log in to add more points →

(117266065309906, 3073679029875028041172)
(241555047802000, 11200344991211074600)
(219009368530500, 623205042126650982900)
(8985470043234687970/38809, 2240578986357384258280099460/7645373)
(4073801710059160, 258685128952480127236240)

Commentary

Dujella - Kazalicki - Peral (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 46). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:11 UTC · history