LMFDB - Elliptic curves over $\Q$ of conductor 349022

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

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Results (21 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	Sato-Tate	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
349022.a1	349022a1	349022.a	349022a	$1$	$1$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{2} \cdot 47^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$		$0$	$844560$	$1.154509$	$4826809/316$	$0.94063$	$3.01582$	$[1, 1, 0, -7777, -251863]$	$y^2+xy=x^3+x^2-7777x-251863$	316.2.0.?	$[ ]$
349022.b1	349022b3	349022.b	349022b	$3$	$9$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{18} \cdot 47^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$133668$	$144$	$3$	$6.232960430$	$1$		$0$	$12270960$	$2.604931$	$15698803397448457/20709376$	$1.00146$	$4.73194$	$[1, 0, 1, -11523295, 15055143922]$	$y^2+xy+y=x^3-11523295x+15055143922$	3.4.0.a.1, 9.12.0.a.1, 141.8.0.?, 316.2.0.?, 423.24.0.?, $\ldots$	$[(158599/9, -686924/9)]$
349022.b2	349022b2	349022.b	349022b	$3$	$9$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{6} \cdot 47^{6} \cdot 79^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	3.12.0.1	3Cs	$133668$	$144$	$3$	$2.077653476$	$1$		$4$	$4090320$	$2.055626$	$59914169497/31554496$	$0.96798$	$3.75441$	$[1, 0, 1, -180080, 8805502]$	$y^2+xy+y=x^3-180080x+8805502$	3.12.0.a.1, 141.24.0.?, 316.2.0.?, 711.36.0.?, 948.24.1.?, $\ldots$	$[(49, 291)]$
349022.b3	349022b1	349022.b	349022b	$3$	$9$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{2} \cdot 47^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$3$	9.12.0.1	3B	$133668$	$144$	$3$	$6.232960430$	$1$		$0$	$1363440$	$1.506319$	$11134383337/316$	$0.90937$	$3.62255$	$[1, 0, 1, -102765, -12688068]$	$y^2+xy+y=x^3-102765x-12688068$	3.4.0.a.1, 9.12.0.a.1, 141.8.0.?, 316.2.0.?, 423.24.0.?, $\ldots$	$[(-4611/5, 12028/5)]$
349022.c1	349022c1	349022.c	349022c	$1$	$1$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{8} \cdot 47^{6} \cdot 79 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$				$316$	$2$	$0$	$1$	$1$		$0$	$3378240$	$1.458496$	$72511713/20224$	$0.89606$	$3.22812$	$[1, -1, 1, -19191, -731697]$	$y^2+xy+y=x^3-x^2-19191x-731697$	316.2.0.?	$[ ]$
349022.d1	349022d2	349022.d	349022d	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{9} \cdot 47^{8} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$29704$	$12$	$0$	$2.372443298$	$1$		$2$	$15261696$	$2.685875$	$2448638586186625/7058620928$	$0.89622$	$4.58636$	$[1, 0, 0, -6202918, -5931925020]$	$y^2+xy=x^3-6202918x-5931925020$	2.3.0.a.1, 8.6.0.b.1, 14852.6.0.?, 29704.12.0.?	$[(6858, 520104)]$
349022.d2	349022d1	349022.d	349022d	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{18} \cdot 47^{7} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$29704$	$12$	$0$	$1.186221649$	$1$		$5$	$7630848$	$2.339298$	$1687284042625/973340672$	$0.92018$	$4.01594$	$[1, 0, 0, -547878, -8836124]$	$y^2+xy=x^3-547878x-8836124$	2.3.0.a.1, 8.6.0.c.1, 7426.6.0.?, 29704.12.0.?	$[(-98, 6676)]$
349022.e1	349022e2	349022.e	349022e	$2$	$5$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{4} \cdot 47^{6} \cdot 79^{5} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.2	5B.4.2	$74260$	$48$	$1$	$16.60323458$	$1$		$0$	$25336800$	$3.067184$	$1413378216646643521/49232902384$	$1.01962$	$5.08454$	$[1, 1, 1, -51646466, 142833648927]$	$y^2+xy+y=x^3+x^2-51646466x+142833648927$	5.12.0.a.2, 235.24.0.?, 316.2.0.?, 1580.24.1.?, 74260.48.1.?	$[(146733763/189, 13571153065/189)]$
349022.e2	349022e1	349022.e	349022e	$2$	$5$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{20} \cdot 47^{6} \cdot 79 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$5$	5.12.0.1	5B.4.1	$74260$	$48$	$1$	$3.320646917$	$1$		$2$	$5067360$	$2.262463$	$8194759433281/82837504$	$0.96131$	$4.13977$	$[1, 1, 1, -927826, -341360673]$	$y^2+xy+y=x^3+x^2-927826x-341360673$	5.12.0.a.1, 235.24.0.?, 316.2.0.?, 1580.24.1.?, 74260.48.1.?	$[(-519, 1107)]$
349022.f1	349022f4	349022.f	349022f	$4$	$4$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2 \cdot 47^{10} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.6	2B	$29704$	$48$	$0$	$61.63943045$	$1$		$0$	$6782976$	$2.449066$	$77619515367393/770989598$	$0.88923$	$4.31593$	$[1, -1, 1, -1963111, -1049065663]$	$y^2+xy+y=x^3-x^2-1963111x-1049065663$	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 376.24.0.?, 632.24.0.?, $\ldots$	$[(401448427508349016930347963/481255038386, 2963123307289307022221003518781451730169/481255038386)]$
349022.f2	349022f2	349022.f	349022f	$4$	$4$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{2} \cdot 47^{8} \cdot 79^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$29704$	$48$	$0$	$30.81971522$	$1$		$2$	$3391488$	$2.102493$	$106294343553/55145476$	$0.90023$	$3.79932$	$[1, -1, 1, -218001, 12659261]$	$y^2+xy+y=x^3-x^2-218001x+12659261$	2.6.0.a.1, 4.12.0-2.a.1.1, 376.24.0.?, 632.24.0.?, 14852.24.0.?, $\ldots$	$[(28454556583787/186839, 123816355074297839406/186839)]$
349022.f3	349022f1	349022.f	349022f	$4$	$4$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{4} \cdot 47^{7} \cdot 79 $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.7	2B	$29704$	$48$	$0$	$15.40985761$	$1$		$3$	$1695744$	$1.755920$	$53881658433/59408$	$0.85285$	$3.74609$	$[1, -1, 1, -173821, 27910197]$	$y^2+xy+y=x^3-x^2-173821x+27910197$	2.3.0.a.1, 4.12.0-4.c.1.1, 376.24.0.?, 632.24.0.?, 7426.6.0.?, $\ldots$	$[(17371161/257, 7585747858/257)]$
349022.f4	349022f3	349022.f	349022f	$4$	$4$	$ 2 \cdot 47^{2} \cdot 79 $	$ - 2 \cdot 47^{7} \cdot 79^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.8	2B	$29704$	$48$	$0$	$61.63943045$	$1$		$0$	$6782976$	$2.449066$	$5661642220767/3661307614$	$0.90224$	$4.11079$	$[1, -1, 1, 820229, 97794121]$	$y^2+xy+y=x^3-x^2+820229x+97794121$	2.3.0.a.1, 4.12.0-4.c.1.2, 376.24.0.?, 632.24.0.?, 29704.48.0.?	$[(249006790728626360665996945/678754698048, 8181646193613483511729695644078935437209/678754698048)]$
349022.g1	349022g2	349022.g	349022g	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{3} \cdot 47^{8} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$29704$	$12$	$0$	$11.72562961$	$1$		$0$	$5935104$	$2.462887$	$4231482925568625/1396088$	$0.91810$	$4.62922$	$[1, -1, 1, -7443640, 7818606979]$	$y^2+xy+y=x^3-x^2-7443640x+7818606979$	2.3.0.a.1, 188.6.0.?, 632.6.0.?, 29704.12.0.?	$[(156547/6, 51399439/6)]$
349022.g2	349022g1	349022.g	349022g	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ - 2^{6} \cdot 47^{7} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.3.0.1	2B	$29704$	$12$	$0$	$5.862814806$	$1$		$3$	$2967552$	$2.116314$	$-1019627024625/18772928$	$1.00436$	$3.97893$	$[1, -1, 1, -463200, 123369923]$	$y^2+xy+y=x^3-x^2-463200x+123369923$	2.3.0.a.1, 94.6.0.?, 632.6.0.?, 29704.12.0.?	$[(-499, 15417)]$
349022.h1	349022h2	349022.h	349022h	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{7} \cdot 47^{12} \cdot 79^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$376$	$12$	$0$	$1$	$16$	$2$	$0$	$249274368$	$4.274605$	$8539859737652459994284625/8610954607140992$	$1.01225$	$6.30795$	$[1, -1, 1, -9406716550, -351157471626347]$	$y^2+xy+y=x^3-x^2-9406716550x-351157471626347$	2.3.0.a.1, 8.6.0.b.1, 188.6.0.?, 376.12.0.?	$[ ]$
349022.h2	349022h1	349022.h	349022h	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ - 2^{14} \cdot 47^{9} \cdot 79^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$376$	$12$	$0$	$1$	$4$	$2$	$1$	$124637184$	$3.928032$	$-2037633332486884268625/66255491230318592$	$1.05373$	$5.65872$	$[1, -1, 1, -583440390, -5574449612395]$	$y^2+xy+y=x^3-x^2-583440390x-5574449612395$	2.3.0.a.1, 8.6.0.c.1, 94.6.0.?, 376.12.0.?	$[ ]$
349022.i1	349022i2	349022.i	349022i	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2 \cdot 47^{6} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$632$	$12$	$0$	$29.16409229$	$1$		$0$	$1271808$	$1.434608$	$81182737/12482$	$0.85973$	$3.23697$	$[1, 1, 1, -19927, -936101]$	$y^2+xy+y=x^3+x^2-19927x-936101$	2.3.0.a.1, 8.6.0.b.1, 316.6.0.?, 632.12.0.?	$[(-198585639600551/1369584, 57764798255327831621/1369584)]$
349022.i2	349022i1	349022.i	349022i	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ - 2^{2} \cdot 47^{6} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$632$	$12$	$0$	$58.32818458$	$1$		$1$	$635904$	$1.088034$	$103823/316$	$0.80009$	$2.82855$	$[1, 1, 1, 2163, -79009]$	$y^2+xy+y=x^3+x^2+2163x-79009$	2.3.0.a.1, 8.6.0.c.1, 158.6.0.?, 632.12.0.?	$[(30331655693608528639548315/24505372351, 166679600079131210408414972549881341262/24505372351)]$
349022.j1	349022j2	349022.j	349022j	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{3} \cdot 47^{8} \cdot 79^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.6	2B	$29704$	$12$	$0$	$21.40748288$	$1$		$0$	$15261696$	$2.157833$	$191202526081/110290952$	$0.90220$	$3.84533$	$[1, 1, 1, -265126, 2881051]$	$y^2+xy+y=x^3+x^2-265126x+2881051$	2.3.0.a.1, 8.6.0.b.1, 14852.6.0.?, 29704.12.0.?	$[(-63034660535/11304, 5746098658395743/11304)]$
349022.j2	349022j1	349022.j	349022j	$2$	$2$	$ 2 \cdot 47^{2} \cdot 79 $	$ 2^{6} \cdot 47^{7} \cdot 79 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.6.0.1	2B	$29704$	$12$	$0$	$42.81496577$	$1$		$1$	$7630848$	$1.811260$	$56667352321/237632$	$0.80807$	$3.75004$	$[1, 1, 1, -176766, -28575109]$	$y^2+xy+y=x^3+x^2-176766x-28575109$	2.3.0.a.1, 8.6.0.c.1, 7426.6.0.?, 29704.12.0.?	$[(10582276567766507745/46752881, 34047207192667683967371035567/46752881)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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