curve #3174

y² + xy = x³ − 7032750154590180472810630714591592198580x + 234825110521164672374627005794918283861649641835073217760400

a-invariants: [1, 0, 0, -7032750154590180472810630714591592198580, 234825110521164672374627005794918283861649641835073217760400]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/3ℤ
conductor (N): 148264132602729384793004314137610218368489339158330295790
discriminant (Δ): -1560146413395583839447076407799434023072364852717128084532735020314925840504183971533927576587833871912423004335616000000
Faltings height: 21.8307
naive height: 286.9355
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 811, 248401, 19194353749, 131873305717
regulator: 584607071344.9335643728198350457041588292666339968109386173234528
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:40:51 UTC
last updated: 2026-09-26 20:40:51 UTC

Witness: 13 independent points log in to add more points →

(55900848433614700560, 127957972604422146757975646220)
(60064561238865449310, 170599150318472748808550606970)
(69812369394041538000, 290002371439954245595102699020)
(61612368528157270560, 188165990173054207603274843220)
(3822294292797501180, 456069855621822797983703355720)
(52372587674097006360, 100766688720822135191405667420)
(51554975084878426920, 96335957098298726629044580620)
(51147073430501124120, 94458713634598078961223670620)
(68932207591190829072, 278538666893854221091708241892)
(47727681973487919720, 88818038537044422433497220620)
(53338169456226155160, 107033016967755131766827494620)
(64102710537148435560, 217749619349148168747134366220)
(52406676754698809160, 100969677496651189732961320620)

Commentary

Eroshkin (2007). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 5). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:40:52 UTC · history