curve #6403

y² = x³ − 457185000605069635567x + 2902407714004269155934326994610

a-invariants: [0, 0, 0, -457185000605069635567, 2902407714004269155934326994610]
c-invariants: [21944880029043342507216, -2507680264899688550727258523343040]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 77396300739231291828456235358756520862785978501077281051455176
discriminant (Δ): 2476681623655401338510599531480208667609151312034472993646565632
Faltings height: 10.8760
naive height: 154.3285
primes of bad reduction: 2, 114207382033, 494460317233, 8685805881979, 19723976564849803736961787
regulator: 10016190589474542681.7483459642353474581909116067231040032032142579522041467414
submitted by: apkorte
submitted at: 2026-11-02 01:53:39 UTC
last updated: 2026-11-02 01:53:39 UTC

Witness: 20 independent points log in to add more points →

(6962303753, 238401568259206)
(5127890029, -832377612512666)
(17116732493, 302981800013894)
(6958839863, 240656340975544)
(18138539837, -759894193764278)
(-1028889279, 1836222008344142)
(21966243249, 1859793307925474)
(23964603959, -2389367289190456)
(-19786763827, 2049825424194106)
(25342086963, -2755288645513544)
(-22206870603, -1450464200156722)
(-21876019533, 1560385453961128)
(6608881802, 411806167868978)
(-7372810970, 2423297861289460)
(-18941013462, -2183263443681706)
(-22788489578, 1219242801106472)
(-36641248807/4, 20114410624664101/8)
(480408535509, -332652802454661394)
(327389504101/49, -131074016506192318/343)
(-838296061151/64, 1319682729967820239/512)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-20-m10-014736.ec), where it is recorded as a find of that challenge; not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.

last edited by apkorte at 2026-11-02 01:53:40 UTC · history