curve #4635

y² = x³ + x² + 3171204129130080087266008689599938752940x + 18620448660185010395729261579161505929155720351269652217935900

a-invariants: [0, 1, 0, 3171204129130080087266008689599938752940, 18620448660185010395729261579161505929155720351269652217935900]
c-invariants: [-152217798198243844188768417100797060141104, -16088067642399848981909168697606351659725409772994374733935770944]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 39074194855695436031173540064661548058671150699483415904066923420321417840
discriminant (Δ): -149785559833392896074121186806285002799152424150460657151820082532247626136753698312579567716845637184428237683058311710048000
Faltings height: 22.6978
naive height: 295.6819
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 29, 43, 61, 83, 181, 277, 331, 359, 389, 601, 647, 829, 1373, 1451, 3847, 13691, 30089, 76679, 106291, 11507869
regulator: 114595158032980052202.42352683806316454703297725891488027077415573636780266
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:32:29 UTC
last updated: 2026-10-19 03:32:29 UTC

Witness: 18 independent points log in to add more points →

(-134503566808194526961, 3969959469598007888787717234120)
(-95737841310464259865862682881/664350625, -66696038965017642201604230401933746011633972/17123637359375)
(339079645397508671890, 7660380125665241452836575608440)
(716478118555599896335, 19715224198656987890577813663720)
(-34678870174901596100438326369310/239626893289, -456278404180169878714069174635544146399862680360/117301437922151413)
(2803861860578303718175, 148561328624548814620382661085980)
(-95963274434974319154567317015/684136336, 70258121146538330354529164113691379772414845/17894270004416)
(105683754710817212222425/1024, 146715258357553460851731695049494685/32768)
(135237681586716140050, 4639257277636698735093964226520)
(-1888172960168716708025/9, 79734483923351979814554225523760/27)
(-11893602936632924689000435693064378194832618690/386381584994677826995672009, -32661500332027785642041617033581577726675034571619443918528252297515520/7594944936087015055202696291901071475973)
(606405952275870158654110/289, 472866390094349781099167287908727080/4913)
(10744916263996345761550/169, 9596409805328551822149756741662760/2197)
(55450673165150661477358/121, 14354799763584954160457287998165576/1331)
(4975797094306957785681072037903/78915484561, -96812373162802614713694241576995843247176310836/22168859007391559)
(3400599144205451965430335/1681, 6280422282358628322548957773636270080/68921)
(168174441453664246372442862424869/1255488876196, -6515083692846477328231979138300092090095007907025/1406757708933351256)
(-101148356141661087249471125071097007755/396821992193343396, -279592315181535487560893000150320112159923738733953682135/249973286244981680816980056)

Commentary

X660, T=3862/585

last edited by Andrii Prokhorenkov at 2026-10-19 03:32:29 UTC · history