curve #3151

y² = x³ − 944350340701979900709096424316569452x + 351982210527405532452913727852239888857539342858675696

a-invariants: [0, 0, 0, -944350340701979900709096424316569452, 351982210527405532452913727852239888857539342858675696]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/4ℤ
conductor (N): 3046788250100588932752869018478456421677120
discriminant (Δ): 377719597552847804493784963884981747527623876489860956027276178891386670115047803145141185265605975357030400
Faltings height: 19.4982
naive height: 260.1210
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 29, 61, 109, 131, 139, 151, 163, 179, 307, 563, 761, 827, 2213, 11423
regulator: 155776617152380.788594478847178587678696835935385675646934119
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:46 UTC
last updated: 2026-09-26 20:39:46 UTC

Witness: 11 independent points log in to add more points →

(38254916231980109305/64, 16777169165426102075826590733/512)
(-18750900605870873341295/21316, 2205015052135300753750914135675609/3112136)
(82535380295061133467062/22801, 22932283690078837935213080092568200/3442951)
(-113875989962068818524408/145161, 43196683471633451523632373497805020/55306341)
(688878499471005282902/121, 17832799164339424213464306070600/1331)
(301838641211894138055389/75625, 161311889604268215124849389013203787/20796875)
(482724803077483366159732/1018081, 106831406043053549774123781730277880/1027243729)
(1670497998040055352029060/3481, 2159076594773081080192801590570282896/205379)
(34077331595867471432087461/286225, 198922518214977527829310211025423289209/153130375)
(-255049975187481208364790218/821338281, 18463838919342848703883023541179689343880/23538733795179)
(-105635307959015288236949372/103286569, 522772318161554324725216926818096493600/1049701400747)

Commentary

Voznyy (2022). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 20). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:46 UTC · history