curve #6240

y² + xy = x³ + x² − 2968849756236562x + 61364311939945727791360

a-invariants: [1, 1, 0, -2968849756236562, 61364311939945727791360]
c-invariants: [142504788299355001, -53018766584899021056897485]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 7999876719625417442633368343888625578394499782
discriminant (Δ): 47999260317752504655800210063331753470366998692
Faltings height: 7.7559
naive height: 118.4945
primes of bad reduction: 2, 3, 1567, 561313, 4437379, 341610666946925529805004012533
regulator: 4662425823827369673.09716522944044686963625787068331948466977945061441868
submitted by: The Wren
submitted at: 2026-10-31 20:36:24 UTC
last updated: 2026-10-31 20:36:24 UTC

Witness: 17 independent points log in to add more points →

(27834502, 17100501442)
(7708809, 197318516207)
(-62814014, -3238317716)
(415075933/16, 2718090753883/64)
(1665672381/169, 399460417270123/2197)
(1791230711, 75774565929530)
(9410266243/169, 575763879478462/2197)
(8163498976, 737568670758424)
(4857573174/289, -625592678575768/4913)
(375693890566/7225, -133985022480188294/614125)
(5518219534/121, 192022960478672/1331)
(421514651/4, 7667508165901/8)
(500652410530/6561, -280801404206172980/531441)
(-418144353870/8281, 216504757844842550/753571)
(-181517285095/3136, -34802885309763425/175616)
(1180784159234/34225, 10862573204305378/6331625)
(3452819206/225, -470334684932066/3375)

Commentary

Original search by i34-9 (2026), public Yukon elliptic-rank challenge submission 7ab99cc9-db1a-4085-aaf6-bae4d565783e, validated 2026-10-31. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/0b63ff3577c4e70ecc2a8df8e5bc7ef3ada5ae89/submission/board/1-17-mestre-10311116.ec . Mestre ten-root construction with roots [0, 8, 13, 32, 50, 53, 54, 63, 76, 103]. The seventeen supplied points were checked exactly on the displayed global minimal model and certified independent modulo torsion by an exact rank-17 F_2 reduction matrix at 24 good primes. The rational torsion subgroup is trivial (the gcd of #E(F_p) over good primes p >= 5 is 1). The complete bad-prime list was verified from the minimal discriminant, with every large factor proved prime.

last edited by The Wren at 2026-10-31 20:36:24 UTC · history