curve #6406

y² + xy + y = x³ − 1035675910631306429844867434648x + 407968979755152500646451395914808650197220006

a-invariants: [1, 0, 1, -1035675910631306429844867434648, 407968979755152500646451395914808650197220006]
c-invariants: [49712443710302708632553636863081, -352485198508451835127199571524457622600853380021]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 112820662312116398359576655670828686730
discriminant (Δ): -804460546842247741910810801304477899361793151691618389579896823729635368338756512125000000
Faltings height: 16.0874
naive height: 218.9627
primes of bad reduction: 2, 3, 5, 7, 11, 13, 41, 59, 61, 71, 131, 251, 10905968613524806738099
regulator: 6911677354711.98676681476904433142904097189859439211185204380
submitted by: Maksym Voznyy
submitted at: 2026-11-02 01:58:49 UTC
last updated: 2026-11-02 01:58:49 UTC

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

(4131497694694271509050105/4315570249, 4860139951332034625513943868417911839/283502756367557)
(-79677410926751172015/108241, -989117646784370539306147777597/35611289)
(51470304076478452620/398161, -4175774897216667494785387517018/251239591)
(-1374725445406057959900855/3266236801, 5177539941433511841761040502266980077/186668699413951)
(40948909883796720, 8283819849288207566561602)
(70303549365487148659173315684345/97123303487762161, -185519609684555592367315795974027309494043614107/30268100596420241470703159)
(4454995235101622993145/4405801, -183703236644259603045044576473327/9247776299)
(118915474644765442020/203401, -139233444289302388347614086373/91733851)
(138064500711922372545/121, -1622268993413912144729484808663/1331)
(-69620361116215, -21902868752921324838573)
(25962240084748946789655/40780996, 671610166292726165181258534470537/260427440456)

Commentary

Voznyy (2026), t = 1369/446 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 01:58:49 UTC · history