curve #6323

y² + xy = x³ − 7117036356200512147x + 7351912716011193949693184289

a-invariants: [1, 0, 0, -7117036356200512147, 7351912716011193949693184289]
c-invariants: [341617745097624583057, -6352052587146098190181348100281]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 19411133257706478263023107221685307117146816645736646
discriminant (Δ): -278278006382480072378699265130080562831416763433280557056
Faltings height: 9.6642
naive height: 141.8527
primes of bad reduction: 2, 7, 1386509518407605590215936230120379079796201188981189
regulator: 9980726422662654.2820632834992259805810240081754217750257267172099455187730
submitted by: The Wren
submitted at: 2026-11-01 00:41:23 UTC
last updated: 2026-11-01 00:41:23 UTC

Witness: 18 independent points log in to add more points →

(1500267630, -7160378243463)
(1462085038, 8466192652025)
(1347336110, -14447525925543)
(1338059374, 14984686252665)
(1625229950, -8828586585767)
(1173625230, -24814417533063)
(1622251030, 8692209313833)
(1953517462, 30061138736961)
(1423676122, 10253127090321)
(847709542, -43908360316783)
(-9903298, 86153321061097)
(1078980494, 30477603892345)
(984305474, -36059144135039)
(1694797592, -12571036404959)
(-547594586, -105284870802039)
(17581664542/9, -811705086823325/27)
(12699726886/9, -294395282710405/27)
(40730083743/4, 7962448605341061/8)

Commentary

Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-18-mestre-11010011.ec, commit 287daf3c0197665eadddf883b1d165a52296433d. Own find: Mestre ten-root construction using quickrank quartic points and the Washington map, roots [0,6,15,25,32,34,38,67,68,85]. The source supplies 18 rational points and marks CLAIM rank=18. This is a Layr-Labs result.

last edited by The Wren at 2026-11-01 00:59:29 UTC · history