curve #2158

y² = x³ − 60335751033640463682x + 19804851792913373013393462044

a-invariants: [0, 0, 0, -60335751033640463682, 19804851792913373013393462044]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 4338664542437869511669258116751422080
discriminant (Δ): 13887927881290229563452022900186116747522773130211773760608000
Faltings height: 10.4219
naive height: 148.2530 ☆ record for ℤ/2ℤ torsion, rank ≥ 13
primes of bad reduction: 2, 3, 5, 31, 37, 43, 79, 137, 229, 317, 647, 653, 1321, 3677, 305551
regulator: 108401861446.3838368015739677351211170743194020015404430187999766
submitted by: Alvaro Lozano-Robledo
submitted at: 2026-09-26 13:22:40 UTC
last updated: 2026-09-26 13:22:40 UTC

Witness: 13 independent points log in to add more points →

(-7328229317, -261556066628685)
(-4635440132, 447084440117910)
(-25327402778154005693/4877206569, 149669551783764555608218866535/340609475159253)
(-154243922745023/85264, 8732921312172152286495/24897088)
(-691082005905369456334942974135283867272045671513373907991084479108625179483111975792032647586564922022449326350199465941197485865521640316453/90107147577428198432354878429866516957305728676753089199454168053062462460579371686072375406423861378996598235606871213182726255049, 4794005621556170858537561855048723523409389380459743701209743767441754572659966273071063637542835003957620584909234845745791382623600828505628191537657778578806338272789098513434748356605260674117856640929245635/27048230757750648407140899696787356075686730832073381229460835714121598222309977109258381221408419737078900723635927675152927907299706408171074748094802776333790481493253664766041016824720845209093)
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(16473956629515019777754424948241232342523589836477410332/73599637552567584187759157169088182804196609, -66824481249337206928030744848556478428597679325816265996022429920061670574004803290/631412991582589738926504229414778447162538947487933796147848110977)
(66246092613697019618628792872491690321750294131760581818893205341502536677562469532252753969001147285450380412/2122492972490833904648096021294850410967290885394791812223865855311271544993357633388268837866863609, 522404908439120005270712765094359850300590323243646791237241883363081262936832781175961050773904758119733568766333657112563128186734969919974809614098002188693599630/97784358611289764396488930496832101895253029750336097854414002451145918974485921706359996900271905502788979602146576173398044113375125421380253662477)

Commentary

This was found searching in a Kihara family. More details will be forthcoming -- or contact the author by email for details.

last edited by Alvaro Lozano-Robledo at 2026-09-26 13:22:40 UTC · history