curve #423

y² + xy = x³ − 277762374045498166503978906288594827838146361987727860020x + 1745716564920954436762537886066484987032789883722113978504519639885660024203054176400

a-invariants: [1, 0, 0, -277762374045498166503978906288594827838146361987727860020, 1745716564920954436762537886066484987032789883722113978504519639885660024203054176400]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 10375475668817043272546748435136605158819777517590828637184232833983229292899320627389321520500291201236878332193594229094587903290
discriminant (Δ): 54982549279076737648560456645555796539139519502785293433793118087871249992058975961811051872139310047478232925568429450545689426273411586773356193898145626236206080000000
Faltings height: 31.3561
naive height: 401.5127
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 41, 59, 61, 67, 83, 223, 21547217, 157359612814219, 74990210119027069803331, 2752170331114714092760458110828021, 8353382291045606203388229504054821
regulator: 478180701956589191634953026719887.8951346280681022033533745771629730037669219016115963550189560
submitted by: 7fff-zip
submitted at: 2026-08-29 17:24:00 UTC
last updated: 2026-08-29 17:24:00 UTC

Witness: 28 independent points log in to add more points →

(11572939538210297926249036140, -284933501046949566847498792181752871585220)
(-1664956572538251656559462200, -1484440454086824476921507616227771472878420)
(2001845575657747452633268451560/9, -2824606335528409560458119212201809313039431740/27)
(609521468511731670002749790460/169, -1953778268571130416332704222278890849943013140/2197)
(30222645496788716316970207960/9, -24905043189764156488715015270168803608948940/27)
(8161152798601958183101916440, -149747108576700892913861958872122791709220)
(8425101742895039879360162440, -59780719709955265608463680480210812563220)
(5302975622946623081989555162, -649520871829255327271395492818624153797138)
(592566150232497683396212090840, -455968920428726192728470212757549357531541220)
(253163027721406175159704513050, 127110304280521124806370600583997991066662830)
(-16166203176414011669963854340, 1418134330768452486622878861568300485275080)
(13644278241428795840547533320, -704240468032998241779412406995127594383220)
(-3998087398100485775706224930, -1671025605207875974707610913372853320169350)
(8255749103293598628866896426, -123573592351217150592726607368988851490658)
(10814321991475872555763684600, -81455601041206593699572658538356842066420)
(11889417300701667679455341800, -352066667409970822948218531770371377218420)
(11570108825205629420190761890, -284317193823990772553886569434379003938970)
(155915105546041762309409613190, -61226299616263392130445595741506397422631470)
(36282922826487822728267446041760600/36481, 6910234711352204129703700188183521155828136248328180/6967871)
(-14078559506945668825588539000504328940/805821769, -25734882352445835918760812786166416008357171278905348560/22874862556603)
(118639623529585438469966715745584232/10751841, -5495497650303636655549018601511889464323999367669196/35255286639)
(771376102508264923607088229808018667475/33590825284, -16834284478663999162101527356232533391276613235380705210835/6156459276400952)
(4588525555063767423537788156950817320/546671161, -960095285830507501022233673253318984520167373099394020/12781718415341)
(8902827702787358007941169013792, 26563860589186567573417837672421538766701642196)
(1998123645447162495070778504285400/151321, -36302033656928181126309355638942836884198504099620/58863869)
(1544111477182209483182449093240/841, 27179486347379773097707729786320522474455429420/24389)
(392578729136908478513198065070440/109561, 32363972848221145310598039985726014604529304713380/36264691)
(19617112714301290098667013012530120/2331729, -234943739026291382497581006858747148836917041579180/3560550183)

Commentary

Found in this search by specializing Noam D. Elkies's rank-17 elliptic K3 family (arXiv:2608.25406) at t=-77087/11609.

last edited by 7fff-zip at 2026-08-29 17:24:00 UTC · history