curve #2138

y² + xy = x³ − 9701467799711167250763437318491625289555x + 367793697914252090667909087517647762075263673985240179857025

a-invariants: [1, 0, 0, -9701467799711167250763437318491625289555, 367793697914252090667909087517647762075263673985240179857025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 168013045163317658634330
discriminant (Δ): 164197158555760770562636451201454793948558123392105440244204034615695613033123793270496208570777862100000
Faltings height: 21.1329
naive height: 287.8329
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 31, 163, 2801, 5059, 3397291
regulator: 18280200.46598523119874816038656010566296768018
submitted by: Steps Unbounded
submitted at: 2026-09-26 10:54:26 UTC
last updated: 2026-09-26 10:54:26 UTC

(19595666895933727923184081169970/344588958289, 205920364186611971150986065301905616885185/202279576527933913)
(801116474743186067288390388/13446889, -1758955715553113369842753692992830737567/49309741963)
(7648840789785330985291703782863111404481515894414534738644498940197680/134151575635778919530088938255673010269835679041441, -3039405276485387306238797526717255929112605900891879823933783174538652613567705481762612718944949363025/1553794811373209208312349929787628603807692141039261980938915689742562324239)
(23882741343073427947490733603870980089851554924450041229937746584796558760/399910104198472782626952823374962673399964296876689641, 9504367746900814652675404505690727400284564087495978736993464259996932612630662161797510370994628248055327405/252896934959770960484141302512752902219818700405219671804692763859353849147340939)

Rational 2-isogenous representative of Fisher's 2016 rank-4 curve with torsion Z/10Z. Quotient taken by the rational point of order 2.

last edited by Steps Unbounded at 2026-09-26 10:54:27 UTC · history