curve #598

y² + xy + y = x³ − x² − 62292126514400052314666336731217x + 189875114844145358895407859631796563863618316609

a-invariants: [1, -1, 1, -62292126514400052314666336731217, 189875114844145358895407859631796563863618316609]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 15016501218675331477327531683556726243855832470296678060577590
discriminant (Δ): -105092742865296124624664670867989090874946904687957351743417680509398873563550183506474240000000
Faltings height: 17.0906
naive height: 231.2485
primes of bad reduction: 2, 3, 5, 7, 17, 19, 37, 41, 71, 109, 223, 10181, 987520084510690916333, 2803586878689814045483
regulator: 29592076255118782.17073903025386670113360497003167178292883348289068516044541
submitted by: wgxli
submitted at: 2026-09-06 11:58:11 UTC
last updated: 2026-09-06 11:58:11 UTC

(4500736576838647, 26161361617660339358516)
(4722898047604567, 31993914076786978512116)
(120145098392238967, -41556968360477998039667884)
(1243678686446787937/121, -1061018462179551451088884934/1331)
(505697151652583807/121, -67019853934980813224409604/1331)
(3828807524511247, -86602418474058078065764)
(4529370805949407, 25532781848420175305876)
(4806097312631347, 38821059315331620298136)
(5134269683318767, -73441205574350704355884)
(-3984767455410233, -612228006691284593357884)
(2734523067863767, -199958928415792548575884)
(477507180002375381479/87025, -2958074529790620569769906643348/25672375)
(83291449261464616028167/17380561, -2723409058277676900574169468224556/72459558809)
(11597273039309270482167139783/2391869485489, -158291364131469428663626295063613663006292/3699186414564266263)
(11092504528774168499153447093/2578648237489, -161151771561346887287182807507840533938542/4140837176779873513)
(17165916872719243/4, -318500167564679866727447/8)
(489212255183312952241387/95433361, -67611345770177139953090556373217356/932288503609)
(170805783644080573052126662327/37086406999321, -5865351489672952961324989185155641029201404/225851063615291984381)
(40101470284836394600122703/8688663369, -21256780140136673028710645340845707388/809896378614597)

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