curve #6261

y² + xy = x³ − x² − 137680325521644667x + 20065242420125692207148641

a-invariants: [1, -1, 0, -137680325521644667, 20065242420125692207148641]
c-invariants: [6608655625038944025, -17336369421249647754301177725]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 1890078571877413719648273191875440370070885076550
discriminant (Δ): -6898786787352560076716197150345357350758730529407500
Faltings height: 8.7330
naive height: 130.0452
primes of bad reduction: 2, 5, 73, 61187353391173, 8463019186486703731252092008039
regulator: 366148311652021.906941870117484656489456530090539188108402759472634836584
submitted by: The Wren
submitted at: 2026-10-31 23:18:45 UTC
last updated: 2026-10-31 23:18:45 UTC

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

(4455663149/16, -116628757248093/64)
(763679444179, -667370258975633782)
(69546973906/225, -8955528126455891/3375)
(1912966569031/324, -2640741091511965469/5832)
(220952335401/1024, 20811333777462299/32768)
(-11054446784/1089, -166484696366970479/35937)
(308266714011/1444, -34810502354298949/54872)
(4511618423349/1936, 9468272905436929427/85184)
(9081398219751/2500, 27229502259070904099/125000)
(137366125, 1935041945121)
(190516114, 865912199723)
(210666450, 640260517979)
(218057554, 641332412603)
(269501384, 1591831965463)
(1630826871/4, 45042705110339/8)
(790146728, 20114061247713)
(-3702700304/9, 71814236156491/27)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 17 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_17.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by The Wren at 2026-10-31 23:18:45 UTC · history