curve #4646

y² + xy = x³ − 37021795523485232884887269294624175x + 2741024867866283901511677387635100120451107601805625

a-invariants: [1, 0, 0, -37021795523485232884887269294624175, 2741024867866283901511677387635100120451107601805625]
c-invariants: [1777046185127291178474588926141960401, -2368245485836469293571658540607663271781640357173000601]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/3ℤ
conductor (N): 14426065733357462829266905296921348827243427570
discriminant (Δ): 1814400193348915817390232690321209551151531147704148883504571047788112251382723783493389234388416000000
Faltings height: 18.5959
naive height: 250.4040
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 41, 43, 59, 67, 71, 127, 311, 1445912685072265605685525099
regulator: 453674179650623.46770145759787456675512135389310376743441116106
submitted by: Maksym Voznyy
submitted at: 2026-10-20 01:26:33 UTC
last updated: 2026-10-20 01:26:33 UTC

Witness: 12 independent points log in to add more points →

(117785535602626632, 3805590396267303967083891)
(1249789436392172738196424134/7298797489, -23516587658620526826503359654418799430491/623558165877737)
(1290288458559974361150/11449, 392372757975613922283712845975/1225043)
(63960019040344507582456642350/567766771009, 98168802695944772305357684951275052770675/427813965255594527)
(379649697787725372047615989902150/3371498121547609, -13560957349139592286770750030906551299353873225/195764699942907662184227)
(14323848423940546231834470/59243809, 40590333473903760725087095204700101485/455999597873)
(4467891045869605935750/32761, 89647364505370782884185694418825/5929741)
(5952516970394843637342119670/52041928129, 20144649475930895227098161897297632284675/11872168938284383)
(98966207091419751998616371159880/870018322421329, 32635690266105932523984678756934188456462126075/25662123949477056941017)
(387348867571704782472586650/1790220721, -5280602866615333911387290525644429641225/75746028926231)
(32417745000492398147088150/196925089, -91971105004081674617108586271458593475/2763449773937)
(152510898314455906752246211050/324955862401, 55183092228422109654354809515951183613173125/185240764405827649)

Commentary

t = 2189/3931 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 2026-10-20 01:26:33 UTC · history