LMFDB - Elliptic curve search results

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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

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Results (25 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	Semistable	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
537.a1	537e1	537.a	537e	$2$	$5$	$ 3 \cdot 179 $	$ - 3^{10} \cdot 179 $	$0$	$\Z/5\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$5$	5.24.0.1	5B.1.1	$1790$	$48$	$1$	$1$	$1$	$4$	$192$	$0.226649$	$-4359504941056/10569771$	$0.94567$	$4.63054$	$[0, 1, 1, -340, 2308]$	$y^2+y=x^3+x^2-340x+2308$	5.24.0-5.a.1.2, 358.2.0.?, 1790.48.1.?	$[]$
1611.h1	1611h1	1611.h	1611h	$2$	$5$	$ 3^{2} \cdot 179 $	$ - 3^{16} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$5370$	$48$	$1$	$3.650876645$	$1$	$0$	$1536$	$0.775955$	$-4359504941056/10569771$	$0.94567$	$4.83427$	$[0, 0, 1, -3063, -65385]$	$y^2+y=x^3-3063x-65385$	5.12.0.a.1, 15.24.0-5.a.1.1, 358.2.0.?, 1790.24.1.?, 5370.48.1.?	$[(1673/2, 67793/2)]$
8592.d1	8592g1	8592.d	8592g	$2$	$5$	$ 2^{4} \cdot 3 \cdot 179 $	$ - 2^{12} \cdot 3^{10} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$3580$	$48$	$1$	$7.336841129$	$1$	$0$	$7680$	$0.919796$	$-4359504941056/10569771$	$0.94567$	$4.13148$	$[0, -1, 0, -5445, -153171]$	$y^2=x^3-x^2-5445x-153171$	5.12.0.a.1, 20.24.0-5.a.1.2, 358.2.0.?, 1790.24.1.?, 3580.48.1.?	$[(23265/4, 3542697/4)]$
13425.j1	13425d1	13425.j	13425d	$2$	$5$	$ 3 \cdot 5^{2} \cdot 179 $	$ - 3^{10} \cdot 5^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.24.0.2	5B.1.4	$1790$	$48$	$1$	$4.203942585$	$1$	$0$	$26880$	$1.031368$	$-4359504941056/10569771$	$0.94567$	$4.07835$	$[0, -1, 1, -8508, 305543]$	$y^2+y=x^3-x^2-8508x+305543$	5.24.0-5.a.1.1, 358.2.0.?, 1790.48.1.?	$[(273/4, 25969/4)]$
25776.i1	25776n1	25776.i	25776n	$2$	$5$	$ 2^{4} \cdot 3^{2} \cdot 179 $	$ - 2^{12} \cdot 3^{16} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$10740$	$48$	$1$	$2.027554245$	$1$	$2$	$61440$	$1.469103$	$-4359504941056/10569771$	$0.94567$	$4.33358$	$[0, 0, 0, -49008, 4184624]$	$y^2=x^3-49008x+4184624$	5.12.0.a.1, 60.24.0-5.a.1.2, 358.2.0.?, 1790.24.1.?, 10740.48.1.?	$[(-215, 2187)]$
26313.a1	26313g1	26313.a	26313g	$2$	$5$	$ 3 \cdot 7^{2} \cdot 179 $	$ - 3^{10} \cdot 7^{6} \cdot 179 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$12530$	$48$	$1$	$1$	$1$	$0$	$69120$	$1.199604$	$-4359504941056/10569771$	$0.94567$	$4.00705$	$[0, -1, 1, -16676, -825070]$	$y^2+y=x^3-x^2-16676x-825070$	5.12.0.a.1, 35.24.0-5.a.1.2, 358.2.0.?, 1790.24.1.?, 12530.48.1.?	$[]$
34368.h1	34368f1	34368.h	34368f	$2$	$5$	$ 2^{6} \cdot 3 \cdot 179 $	$ - 2^{6} \cdot 3^{10} \cdot 179 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$7160$	$48$	$1$	$2.120439586$	$1$	$6$	$15360$	$0.573222$	$-4359504941056/10569771$	$0.94567$	$3.18495$	$[0, -1, 0, -1361, 19827]$	$y^2=x^3-x^2-1361x+19827$	5.12.0.a.1, 40.24.0-5.a.1.3, 358.2.0.?, 1790.24.1.?, 7160.48.1.?	$[(101/2, 243/2), (86, 729)]$
34368.bm1	34368by1	34368.bm	34368by	$2$	$5$	$ 2^{6} \cdot 3 \cdot 179 $	$ - 2^{6} \cdot 3^{10} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$7160$	$48$	$1$	$1.944663235$	$1$	$2$	$15360$	$0.573222$	$-4359504941056/10569771$	$0.94567$	$3.18495$	$[0, 1, 0, -1361, -19827]$	$y^2=x^3+x^2-1361x-19827$	5.12.0.a.1, 40.24.0-5.a.1.1, 358.2.0.?, 1790.24.1.?, 7160.48.1.?	$[(76, 567)]$
40275.c1	40275v1	40275.c	40275v	$2$	$5$	$ 3^{2} \cdot 5^{2} \cdot 179 $	$ - 3^{16} \cdot 5^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$5370$	$48$	$1$	$5.576671418$	$1$	$0$	$215040$	$1.580673$	$-4359504941056/10569771$	$0.94567$	$4.27745$	$[0, 0, 1, -76575, -8173094]$	$y^2+y=x^3-76575x-8173094$	5.12.0.a.1, 15.24.0-5.a.1.2, 358.2.0.?, 1790.24.1.?, 5370.48.1.?	$[(8359/5, 237227/5)]$
64977.j1	64977j1	64977.j	64977j	$2$	$5$	$ 3 \cdot 11^{2} \cdot 179 $	$ - 3^{10} \cdot 11^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$19690$	$48$	$1$	$5.310494420$	$1$	$0$	$268800$	$1.425596$	$-4359504941056/10569771$	$0.94567$	$3.92490$	$[0, 1, 1, -41180, -3236953]$	$y^2+y=x^3+x^2-41180x-3236953$	5.12.0.a.1, 55.24.0-5.a.1.1, 358.2.0.?, 1790.24.1.?, 19690.48.1.?	$[(4105/4, 113587/4)]$
78939.s1	78939r1	78939.s	78939r	$2$	$5$	$ 3^{2} \cdot 7^{2} \cdot 179 $	$ - 3^{16} \cdot 7^{6} \cdot 179 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$37590$	$48$	$1$	$1$	$1$	$0$	$552960$	$1.748909$	$-4359504941056/10569771$	$0.94567$	$4.20121$	$[0, 0, 1, -150087, 22426969]$	$y^2+y=x^3-150087x+22426969$	5.12.0.a.1, 105.24.0.?, 358.2.0.?, 1790.24.1.?, 37590.48.1.?	$[]$
90753.k1	90753i1	90753.k	90753i	$2$	$5$	$ 3 \cdot 13^{2} \cdot 179 $	$ - 3^{10} \cdot 13^{6} \cdot 179 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$23270$	$48$	$1$	$1$	$1$	$0$	$449280$	$1.509123$	$-4359504941056/10569771$	$0.94567$	$3.89783$	$[0, 1, 1, -57516, 5301209]$	$y^2+y=x^3+x^2-57516x+5301209$	5.12.0.a.1, 65.24.0-5.a.1.1, 358.2.0.?, 1790.24.1.?, 23270.48.1.?	$[]$
96123.i1	96123i1	96123.i	96123i	$2$	$5$	$ 3 \cdot 179^{2} $	$ - 3^{10} \cdot 179^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$1790$	$48$	$1$	$11.73606089$	$1$	$0$	$6151680$	$2.820343$	$-4359504941056/10569771$	$0.94567$	$5.24970$	$[0, 1, 1, -10904620, -13892661047]$	$y^2+y=x^3+x^2-10904620x-13892661047$	5.12.0.a.1, 10.24.0-5.a.1.1, 358.2.0.?, 895.24.0.?, 1790.48.1.?	$[(78476413/42, 693233303617/42)]$
103104.bx1	103104k1	103104.bx	103104k	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 179 $	$ - 2^{6} \cdot 3^{16} \cdot 179 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$21480$	$48$	$1$	$1$	$1$	$0$	$122880$	$1.122528$	$-4359504941056/10569771$	$0.94567$	$3.45286$	$[0, 0, 0, -12252, -523078]$	$y^2=x^3-12252x-523078$	5.12.0.a.1, 120.24.0.?, 358.2.0.?, 1790.24.1.?, 21480.48.1.?	$[]$
103104.cd1	103104cr1	103104.cd	103104cr	$2$	$5$	$ 2^{6} \cdot 3^{2} \cdot 179 $	$ - 2^{6} \cdot 3^{16} \cdot 179 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$21480$	$48$	$1$	$1$	$1$	$0$	$122880$	$1.122528$	$-4359504941056/10569771$	$0.94567$	$3.45286$	$[0, 0, 0, -12252, 523078]$	$y^2=x^3-12252x+523078$	5.12.0.a.1, 120.24.0.?, 358.2.0.?, 1790.24.1.?, 21480.48.1.?	$[]$
155193.a1	155193a1	155193.a	155193a	$2$	$5$	$ 3 \cdot 17^{2} \cdot 179 $	$ - 3^{10} \cdot 17^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$30430$	$48$	$1$	$2.317201552$	$1$	$2$	$967680$	$1.643255$	$-4359504941056/10569771$	$0.94567$	$3.85753$	$[0, -1, 1, -98356, 11930388]$	$y^2+y=x^3-x^2-98356x+11930388$	5.12.0.a.1, 85.24.0.?, 358.2.0.?, 1790.24.1.?, 30430.48.1.?	$[(121, 1336)]$
193857.e1	193857e1	193857.e	193857e	$2$	$5$	$ 3 \cdot 19^{2} \cdot 179 $	$ - 3^{10} \cdot 19^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$34010$	$48$	$1$	$52.43402701$	$1$	$0$	$1296000$	$1.698868$	$-4359504941056/10569771$	$0.94567$	$3.84186$	$[0, -1, 1, -122860, -16569195]$	$y^2+y=x^3-x^2-122860x-16569195$	5.12.0.a.1, 95.24.0.?, 358.2.0.?, 1790.24.1.?, 34010.48.1.?	$[(641043904964587718251921/37265764100, 258019780028303812953721298696952719/37265764100)]$
194931.c1	194931c1	194931.c	194931c	$2$	$5$	$ 3^{2} \cdot 11^{2} \cdot 179 $	$ - 3^{16} \cdot 11^{6} \cdot 179 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$59070$	$48$	$1$	$2.269003257$	$1$	$10$	$2150400$	$1.974903$	$-4359504941056/10569771$	$0.94567$	$4.11207$	$[0, 0, 1, -370623, 87027102]$	$y^2+y=x^3-370623x+87027102$	5.12.0.a.1, 165.24.0.?, 358.2.0.?, 1790.24.1.?, 59070.48.1.?	$[(320, 1093), (341, 544)]$
214800.bu1	214800i1	214800.bu	214800i	$2$	$5$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 179 $	$ - 2^{12} \cdot 3^{10} \cdot 5^{6} \cdot 179 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$3580$	$48$	$1$	$1$	$1$	$0$	$1075200$	$1.724514$	$-4359504941056/10569771$	$0.94567$	$3.83483$	$[0, 1, 0, -136133, -19418637]$	$y^2=x^3+x^2-136133x-19418637$	5.12.0.a.1, 20.24.0-5.a.1.1, 358.2.0.?, 1790.24.1.?, 3580.48.1.?	$[]$
272259.b1	272259b1	272259.b	272259b	$2$	$5$	$ 3^{2} \cdot 13^{2} \cdot 179 $	$ - 3^{16} \cdot 13^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$69810$	$48$	$1$	$10.80289662$	$1$	$0$	$3594240$	$2.058430$	$-4359504941056/10569771$	$0.94567$	$4.08238$	$[0, 0, 1, -517647, -143650296]$	$y^2+y=x^3-517647x-143650296$	5.12.0.a.1, 195.24.0.?, 358.2.0.?, 1790.24.1.?, 69810.48.1.?	$[(2098001/22, 2993969245/22)]$
284073.e1	284073e1	284073.e	284073e	$2$	$5$	$ 3 \cdot 23^{2} \cdot 179 $	$ - 3^{10} \cdot 23^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$41170$	$48$	$1$	$1.257435204$	$1$	$4$	$2365440$	$1.794395$	$-4359504941056/10569771$	$0.94567$	$3.81624$	$[0, 1, 1, -180036, -29524318]$	$y^2+y=x^3+x^2-180036x-29524318$	5.12.0.a.1, 115.24.0.?, 358.2.0.?, 1790.24.1.?, 41170.48.1.?	$[(567, 7141)]$
288369.b1	288369b1	288369.b	288369b	$2$	$5$	$ 3^{2} \cdot 179^{2} $	$ - 3^{16} \cdot 179^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$5370$	$48$	$1$	$4.423387311$	$1$	$2$	$49213440$	$3.369648$	$-4359504941056/10569771$	$0.94567$	$5.31527$	$[0, 0, 1, -98141583, 375003706680]$	$y^2+y=x^3-98141583x+375003706680$	5.12.0.a.1, 30.24.0-5.a.1.1, 358.2.0.?, 1790.24.1.?, 2685.24.0.?, $\ldots$	$[(6599, 121378)]$
421008.bv1	421008bv1	421008.bv	421008bv	$2$	$5$	$ 2^{4} \cdot 3 \cdot 7^{2} \cdot 179 $	$ - 2^{12} \cdot 3^{10} \cdot 7^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$25060$	$48$	$1$	$1.015609514$	$1$	$4$	$2764800$	$1.892752$	$-4359504941056/10569771$	$0.94567$	$3.79145$	$[0, 1, 0, -266821, 53071283]$	$y^2=x^3+x^2-266821x+53071283$	5.12.0.a.1, 140.24.0.?, 358.2.0.?, 1790.24.1.?, 25060.48.1.?	$[(254, 1323)]$
451617.g1	451617g1	451617.g	451617g	$2$	$5$	$ 3 \cdot 29^{2} \cdot 179 $	$ - 3^{10} \cdot 29^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$51910$	$48$	$1$	$11.76858990$	$1$	$0$	$4704000$	$1.910297$	$-4359504941056/10569771$	$0.94567$	$3.78718$	$[0, -1, 1, -286220, 59157209]$	$y^2+y=x^3-x^2-286220x+59157209$	5.12.0.a.1, 145.24.0.?, 358.2.0.?, 1790.24.1.?, 51910.48.1.?	$[(2476241/68, 2418533807/68)]$
465579.o1	465579o1	465579.o	465579o	$2$	$5$	$ 3^{2} \cdot 17^{2} \cdot 179 $	$ - 3^{16} \cdot 17^{6} \cdot 179 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$5$	5.12.0.1	5B.4.1	$91290$	$48$	$1$	$75.10258352$	$1$	$0$	$7741440$	$2.192562$	$-4359504941056/10569771$	$0.94567$	$4.03788$	$[0, 0, 1, -885207, -321235277]$	$y^2+y=x^3-885207x-321235277$	5.12.0.a.1, 255.24.0.?, 358.2.0.?, 1790.24.1.?, 91290.48.1.?	$[(14018251677777604351531973483067409/3130699792493278, 1122573670623596980376360741805239775448082515902061/3130699792493278)]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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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