curve #2734

y² + xy = x³ − 1811176602147609970144604336711266625551295x + 900488389630396588157147423615658892099001345086675766227088025

a-invariants: [1, 0, 0, -1811176602147609970144604336711266625551295, 900488389630396588157147423615658892099001345086675766227088025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 10344178476746183675100326370
discriminant (Δ): 29944126318009522061008632142418316298700269399955227192873406083045720967701903218221141650973953316540992640955367490294400000
Faltings height: 23.2223
naive height: 303.5213
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 47, 59, 61, 89, 139, 2069, 5981, 442271
regulator: 5697446.096509431835613684344855346540935672590
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:19:55 UTC
last updated: 2026-09-26 20:19:55 UTC

Witness: 4 independent points log in to add more points →

(197079459824218474722104566638454/117796536225, -2042922399233834272359628659624888050127522266797/40429538180463375)
(421505620680076677867465954570372074843692/668611550978914316761, -52536706290993329172076951736938507871285568836728355208704581/17288639272248697457136247620509)
(156534098061080284105664952573322380399271217920/982611306736401655700343889, -764476441682524175190203904918915584701382124282281877067136379209921405/30801554545322255785819642080688666346713)
(11006288954559141477268668850766889242085010339785664246134646690/8423607433116667161279432336307739839241209, -676044497705043072003296505972075667138707142703212040793841984264147570558375589816339555833055/24448216270997245951441497823188132131501073247272540359579921677)

Commentary

2-isogenous image of D-z10-016, rational kernel x=773507848541288941990. Source: https://dujella.github.io/tors/z10.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:19:55 UTC · history