curve #309

y² + xy + y = x³ − 139247897426027149067804108174260263825601x − 12171148262466750740691943470052015013728330466029726884498652

a-invariants: [1, 0, 1, -139247897426027149067804108174260263825601, -12171148262466750740691943470052015013728330466029726884498652]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 14736232836353426730586889330999407111621750064300242106070930802493850
naive height: 295.8248
Faltings height: 22.6927
discriminant (Δ): 108805746048883061193612306928010127310531083533286108872721769647652556904158900879842993759008627125609908132164015812250000
primes of bad reduction: 2, 3, 5, 7, 17, 23, 37, 41, 67, 79, 97, 101, 103, 151, 229, 389, 857, 977, 983, 1499, 1531, 11719, 12907, 49639, 938573, 4153367
regulator: 474127480377383785864.20755223411635893132159742175014720820682659761
submitted by: 7fff-zip
submitted at: 2026-08-24 00:23:34 UTC
last updated: 2026-08-24 00:23:34 UTC

(417476533381735876627, -1567389922802024902616992663114)
(13580713215478598882323, -1582044898771593034949712886747018)
(35729115842572740083857/64, 4694856465890330255585827438133083/512)
(-6831837002591247631847/64, 622205546465850731255887962212257/512)
(45217890518455797390553/64, -7967061107978184542849544737310143/512)
(-213293129493828877917353/961, 83208523138046682258484816354057826/29791)
(346002499441700055197692/121, 201731669795856202671162628019538241/1331)
(56977374367393099737748/121, -6873807449291231757042867567962288/1331)
(4010446973304367153050763/169, 8030364686397976757935409794061557742/2197)
(9381785176543140026035759/169, -28735476228620029072986061579098599626/2197)
(1462525692414421670628763/1369, 1647849426236391674372613810260726558/50653)
(-5679055972988851923621653/26569, -12116070391266908198024640288072161902/4330747)
(-1121581080347924732470229/3721, 352795474595347348115654922139783886/226981)
(-46416368114055357305883497/146689, 25626148534805874399586744718663739382/56181887)
(-382777754516683952410076/1369, -112172516271497474124380291760240049/50653)

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