curve #3162

y² = x³ − 71016450598376685828738822609116652x + 7262019996454072966062130364617906017922660966355696

a-invariants: [0, 0, 0, -71016450598376685828738822609116652, 7262019996454072966062130364617906017922660966355696]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/4ℤ
conductor (N): 1960485463586913342377444285725055962941120
discriminant (Δ): 139874089674325965176789954683129871469847031866776134897275461245660765779539023858030774526439280640000
Faltings height: 18.8458
naive height: 252.3583
primes of bad reduction: 2, 3, 5, 7, 23, 29, 37, 59, 79, 83, 107, 241, 293, 317, 397, 421, 1933, 3067, 4291829
regulator: 51821131481161.2482091121654413556774048979809771525849739316
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:40:15 UTC
last updated: 2026-09-26 20:40:15 UTC

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

(590570941802758957, 413881117676024094193872915)
(486460870147091782, 296367050257566784853447160)
(93068439245587659286/25, 895609680842394633167167157784/125)
(13633090461214947622/81, 6403866092638841715230090440/729)
(22832849567776951798/169, 25380126005861616020352158040/2197)
(-3945302181194111383/16, 6329408988650232042162538315/64)
(32669525469732318327541/185761, 1165818454502900530104418402049265/80062991)
(-65114466074481061191242/413449, 32056601099762566609947153300588840/265847707)
(3726052363107527062, 7174480684765838367651735960)
(-1662524697198869271565802/16104169, 7506976486515505378148934374734803240/64626030197)
(2504026697401386137958790/18412681, 863047192812114567750670212901106184/79008814171)

Commentary

Voznyy (2022). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 21). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:40:15 UTC · history