curve #1871

y² + xy + y = x³ − x² − 2098752329156516720309919652447928572962x + 36453013198670586168707971603982126833836416792804820566049

a-invariants: [1, -1, 1, -2098752329156516720309919652447928572962, 36453013198670586168707971603982126833836416792804820566049]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 372327578578974140927219420914139947307665232040759399661876110536101542864354222243432448130
discriminant (Δ): 17597021688121615517849721685717003450957998351890675425992642969482961006764159319582318900482562667099520093593600000
Faltings height: 21.4864
naive height: 283.2401
primes of bad reduction: 2, 5, 7, 11, 13, 17, 23, 31, 41, 47, 131, 3049, 3986963341653855186678991779301659573988629210171645437507575782335557916081
regulator: 7319723710413470338280997.8442377842571180882588007542917984264247724938923614448556023
submitted by: Ritik Jain
submitted at: 2026-09-25 17:21:28 UTC
last updated: 2026-09-25 17:21:28 UTC

Witness: 24 independent points log in to add more points →

(1839671294089790042495977/20736, -2211564875460584401429751428559210611/2985984)
(23331157442458121464826759181943794756073/10818369551989201451209, -201089122696038377781069786026853869667354863052849295243503813/1125233670355165066970574979116677)
(410406452178186599113/9, 5092323872862022787442270816517/27)
(33296465101990534209, 59044545220696088017664449503)
(-23310004897605502703, -269646623545430899671902932929)
(45126411632522226217, 183409273605216304424134203471)
(1769745837764746178601/25, -61571190550329621920941391792189/125)
(35250760298086210097, 79205809480958040750024837071)
(263810603152668838153/9, 294781059604248128316093067717/27)
(1219758659593636446866857/19881, 1043734059508513048375593078364074251/2803221)
(442955615603176742473/9, -6179355997254456182325096969083/27)
(35651199671327743077553/1521, -695046367311345616306261927422103/59319)
(43207253843327707857, -162584979696699645070605163329)
(297108260932248656518057/9801, -25454215311395677660105968890753371/970299)
(-36502858656206037743, -253820648462549986409674708929)
(23349046847326358469, -13361629479988428334002688173)
(34104867368427419329, -67410283144966290823448804897)
(-40959797118353186623, 231730505561503078567302485471)
(23463014689076102997, 11253996805177116970163407431)
(17259727547622236897, 73285479388268575532038576031)
(323085058320009307875847310773/21540552289, 288857284816042193189530495841771506914862573/3161442237799663)
(152065186458616376982218237/7134241, 713567517108464856969446319046287800581/19055557711)
(15574015559907508739533886140033/943107072769, 72687001340940053366291425824078662861528951263/915886173327668353)
(-57244545243965663463994382623410693/14505952340354281, 369271609466938750089465561207913140662992933179313799/1747106459294861897111179)

Commentary

No commentary yet.