curve #393

y² + xy + y = x³ − x² − 1741982199429864469286704668873479663123369747x + 33616270057492031684630745788339880287409192129638100252550440305971

a-invariants: [1, -1, 1, -1741982199429864469286704668873479663123369747, 33616270057492031684630745788339880287409192129638100252550440305971]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 119549621982267876087515714877349379640427255973867059607509463471902295421812627301510771993637447925758290 ★ record for rank ≥ 26
naive height: 324.4944
Faltings height: 25.0389
discriminant (Δ): -149876060553927707457112170675614455908665133076577521548424090262727766934501775562130754896641736169261092596472896710393678952857600000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 59, 107, 7717, 2240241213160292084959823237590027825914589, 2214323680021789291529522005032731234353253385439
regulator: 36363952729145652570683632115.2765867078594972317037961267999440429399427534681151028919678
submitted by: wgxli
submitted at: 2026-08-27 19:44:30 UTC
last updated: 2026-08-27 19:44:30 UTC

Witness: 26 independent points

(1374865390985581150009337351939699973611/44032825180320001, 28726373821149914873664438220203601527392175166338809846206/9239847991805523829519999)
(-2267857005598203636591509/81, -5667516638884584255637878592095500174/729)
(-2410502861707362438433885/49, -174820341176673826779087223600403834/343)
(26090796201646469047301, -2434614133474070076590565289434916)
(678734235089795731242289490066375035/31757631722881, 443766389494574248319309709112202263969352300543845822/178966671992438081471)
(364269508642940102735611, -218482985741789370821273623263561406)
(377928556836390393647515/9, 158618612062380850912755077404809694/27)
(13384123300342651927329571/81, -47565298738588723788772387683253428814/729)
(164993183065107141202159/9, 75612161056655848263729777490747378/27)
(33820172762628110067859, -3658658621441229865168387239817366)
(28331032987816465306499, -2646496877513231969224749791147654)
(1669227683953389365241085101708139/119720844049, 143729732610230254326394610797593951100371904636942/41424250086862343)
(151853747842668350473901547460339/3312808249, -1349359477305796459634155354438676103723531069158/190675304387693)
(28634813210961415170791, 2685911880603313612329557546181574)
(619988330384556463865666977748065/15986314969, -9982200266325867291153364151911501836605228776394/2021261705735453)
(48801418949749495528106491/961, 259902562182049537716685989912623022974/29791)
(495911546737595211946099/25, 327558704994372363916107591325843258/125)
(1772525446758752397606699460925509518024056060101091/16961072224809426887749651321, 69604325007888308707883552984844748171606492166608048173212249025271960441126/2208919836452982430892590007374940856957619)
(525150493308888865436219918661795725175434675971/4774160419611124338105241, 357260173619921119849532925673369014055377212099468806718801649510028346/10431469963491244233810980803932505789)
(2361327826858467851967002313721230210968166019/1857622815979504850329, 114684244909771071927131528214446047394816022080869970341372098505402/80063819554504070434022532364733)
(223918645815601696540248914836884494971/694134426437761, 3324226900254655967803825911359668502040985921403670670654/18287964770867045980991)
(7132155633535605849104118220241213732374437059/24817781138900714836369, 596370298976713003705938431911904239460284820141827682760615921818482/3909708923129257102282242145268153)
(1220520692197966008693133168097896004904979/3496910423387767369, 1339258151984867315694515958717546610178078086977164647926722102/6539232237624474961737657403)
(238078060891176639024126239181140118779/3995850245456644, 3002900390641481202630845382854729827206226508328205079573/252588634653286527531272)
(28836398984061130885693319712139685378133317419/1401389546821816206769, -4896780603589960865837439842237241848065277274946887088199818233814802/52461210885041783196445228794647)
(2706465577038366919533700270748878377109/4198675572707344, -140513756954416405224550437358549276138323945316730867642507/272062370435725438148672)

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