curve #311

y² + xy = x³ − 47272342688123468294792417941461088407840527939755x − 42941508837775730432220302570878099751385660941354601764714541918970825039

a-invariants

[1, 0, 0, -47272342688123468294792417941461088407840527939755, -42941508837775730432220302570878099751385660941354601764714541918970825039]

c-invariants

[2269072449029926478150036061190132243576345341108241, 37101463635838231093438338017630004640307493828276284139514998853472781171335]

rank (lower bound)

≥ 18

torsion subgroup

ℤ/2ℤ

conductor (N)

25725142933318819706009609339333397294766021498979988120833604560475705134314952598

discriminant (Δ)

5964254353060440281776945916503620086821580011305699112141314114279612506639005884799439060156150387371657313705870470386745717322956901121284033068032

Faltings height

27.6235

naive height

354.7536

primes of bad reduction

2, 3, 7, 11, 17, 29, 31, 41, 47, 53, 79, 107, 109, 137, 149, 181, 313, 487, 2063, 3209, 3329, 6469, 10513, 15091, 18913, 23417, 32441, 47051, 131749, 643889

regulator

2560205152598496888093876.5106890749802037874182228323879555321467258755327

submitted by

7fff-zip

submitted at

2026-08-24 00:23:49 UTC

later contributions

rank ≥ 15 → ≥ 18 · David Renshaw · 2026-09-02 19:09:07 UTC

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

(61764401751121059885310958, 482347076966160194274310585188683105489)
(76036685752527470559988976, 660283744951403971816311684149448282713)
(89873999762568780808944086, 849500431278140257468645519177290475001)
(-53451965606910845350988731327264656562/8887142039161, 129267943183799720116752940015496454233131072333609946099/26493734634346071091)
(-23551396175780600938996915790830084834/7622695811929, 180575972107712831714586476939769903012267919645981455667/21045676189158450467)
(-7267435845046296299360943059333869670/2981247703641, 39137662033325083801683246681460543399134172536470611849/5147508741289956189)
(-4540181174313244498711224152017802666/3598832849481, 26165202050900770478683671925860422757716835118039411435/6827198246603576379)
(-23199704331201908910092677955318/8625969, 203849907081820003229560116065835452272221058469/25334470953)
(-18207131489440094516692477426/16129, 6139389029237655331395343132941565107243023/2048383)
(-1167841351414754739093622162/361, 59846414539368939637548050399885832623051/6859)
(-201523342589791079432589178/49, 3104328774987529084682840561034912852239/343)
(68178358232335267435787680/9, 156682203368537514423219138429164640067/27)
(450127354986660415882556542/9, 9457669964199156712535423378909848181483/27)
(594067569078630391632906706654/5041, 457096246277436683917002261099116583769872791/357911)
(86440978433262708542333920696286/6295081, 687929959143048310407641688707037205436391264149/15794358229)
(132487782070397616518835531983944/12215025, 1145780257675531137013428452887176899351426702713/42691512375)
(513228323883079838138477811478322282/62353585849, 174492932759008278736083207813637291745574624998265367/15570126861596243)
(4057680848419795853058943368859431396885026/226421993530916401, 7515085822460930624424460107606186436711886155497789423185134513/107740234068584898133234601)

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