curve #3044

y² + xy = x³ − 2035100211022863701787786128710x + 1119278596873289775178978177109549448664136036

a-invariants: [1, 0, 0, -2035100211022863701787786128710, 1119278596873289775178978177109549448664136036]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 251917139582171073862154486898
discriminant (Δ): -1770110213594331323167102207328513150861043856231378625553756998094394761298316431442608128
Faltings height: 16.2068
naive height: 220.9812
primes of bad reduction: 2, 3, 11, 13, 17, 19, 23, 31, 41, 43, 53, 43272041, 315313681
regulator: 35387016.0825821287290435053665230097073506364572475709
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:40 UTC
last updated: 2026-09-26 20:34:40 UTC

Witness: 8 independent points log in to add more points →

(809950927023548, 1513839045447279408794)
(-446118717105622, -44027122021549503042712)
(-623216343019402, -46319865260069317453042)
(1524732508526966, 39509584717306285999886)
(222918649359098, 26013347260427440651694)
(2966841354706604, 145588578806883134944490)
(12017719313709164, 1308559533193737710183210)
(716892025238444, 5363468406693209966186)

Commentary

Dujella - Lecacheux - Petricevic (2021). Source: https://dujella.github.io/tors/z5old678.html (curve entry 10). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:40 UTC · history