curve #6404

y² + xy + y = x³ − x² − 24875000000533463487371823634907x + 47757331066252382301807291043809820061634860939

a-invariants: [1, -1, 1, -24875000000533463487371823634907, 47757331066252382301807291043809820061634860939]
c-invariants: [1194000000025606247393847534475521, -41262334041242052935761499346623571260938614711681]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 901664288415764255908633877077197519630
discriminant (Δ): -214598623568960377300737684022842098770639306250105321318775394254866287477577032138752000000
Faltings height: 16.7390
naive height: 228.4881
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 41, 163, 173, 1153, 1453, 19477, 1920637, 3633187
regulator: 27235329425830.5486840816467251936513524601916960414731322811
submitted by: Maksym Voznyy
submitted at: 2026-11-02 01:55:21 UTC
last updated: 2026-11-02 01:55:21 UTC

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

(30333136381321365723/10609, 3235163646290284980842635702/1092727)
(1102514910753018857322514310247643/391183871002681969, 1493118015519061903802305196510705648497182389578/244664753922430556296178953)
(320731523074408360747, -5743974059372783425366545054374)
(777269181496253058259/225625, 5818827576689438034533614134702/107171875)
(220150786313071747/81, 10974123084505565212948394/729)
(-309133666818613313338613/128346241, -445081977051639489100809053067934086/1454034564289)
(8808741089075644227/1681, 17064100948807516957350642026/68921)
(8506042330543990063739483761828765227/3040847884263227007841, -1332078886479136421682689250146334522871097345285695514/167684161382848284810804107296111)
(48913447896236128867/17161, 7970646325066799332735494366/2248091)
(5046244705261439075271522843/1794804128209, 16087211078998651177716819966384870772502/2404504474973981927)
(550615465900847280922234533/175651515664, 1779531504550943557426178574460497657887/73616955426907712)

Commentary

Voznyy (2026), t = 1959/1499 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec

last edited by Maksym Voznyy at 2026-11-02 01:55:21 UTC · history