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 (24 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	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
2072.d1	2072b1	2072.d	2072b	$1$	$1$	$ 2^{3} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$0.476975638$	$1$	$4$	$192$	$-0.393622$	$27648/259$	$0.75618$	$2.42173$	$[0, 0, 0, 4, -12]$	$y^2=x^3+4x-12$	518.2.0.?	$[(2, 2)]$
4144.e1	4144c1	4144.e	4144c	$1$	$1$	$ 2^{4} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$384$	$-0.393622$	$27648/259$	$0.75618$	$2.22020$	$[0, 0, 0, 4, 12]$	$y^2=x^3+4x+12$	518.2.0.?	$[]$
14504.c1	14504b1	14504.c	14504b	$1$	$1$	$ 2^{3} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37 $	$2$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$0.370845926$	$1$	$16$	$9216$	$0.579333$	$27648/259$	$0.75618$	$3.14839$	$[0, 0, 0, 196, 4116]$	$y^2=x^3+196x+4116$	518.2.0.?	$[(14, 98), (42, 294)]$
16576.i1	16576c1	16576.i	16576c	$1$	$1$	$ 2^{6} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$3072$	$-0.047049$	$27648/259$	$0.75618$	$2.33147$	$[0, 0, 0, 16, -96]$	$y^2=x^3+16x-96$	518.2.0.?	$[]$
16576.j1	16576p1	16576.j	16576p	$1$	$1$	$ 2^{6} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$3072$	$-0.047049$	$27648/259$	$0.75618$	$2.33147$	$[0, 0, 0, 16, 96]$	$y^2=x^3+16x+96$	518.2.0.?	$[]$
18648.b1	18648ba1	18648.b	18648ba	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7 \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$0.603627388$	$1$	$6$	$6144$	$0.155684$	$27648/259$	$0.75618$	$2.55094$	$[0, 0, 0, 36, 324]$	$y^2=x^3+36x+324$	518.2.0.?	$[(0, 18)]$
29008.h1	29008c1	29008.h	29008c	$1$	$1$	$ 2^{4} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 7^{7} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$18432$	$0.579333$	$27648/259$	$0.75618$	$2.93601$	$[0, 0, 0, 196, -4116]$	$y^2=x^3+196x-4116$	518.2.0.?	$[]$
37296.g1	37296bc1	37296.g	37296bc	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7 \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1.554065373$	$1$	$2$	$12288$	$0.155684$	$27648/259$	$0.75618$	$2.38297$	$[0, 0, 0, 36, -324]$	$y^2=x^3+36x-324$	518.2.0.?	$[(9, 27)]$
51800.n1	51800p1	51800.n	51800p	$1$	$1$	$ 2^{3} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$20736$	$0.411097$	$27648/259$	$0.75618$	$2.59320$	$[0, 0, 0, 100, -1500]$	$y^2=x^3+100x-1500$	518.2.0.?	$[]$
76664.a1	76664g1	76664.a	76664g	$1$	$1$	$ 2^{3} \cdot 7 \cdot 37^{2} $	$ - 2^{8} \cdot 7 \cdot 37^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$262656$	$1.411837$	$27648/259$	$0.75618$	$3.57053$	$[0, 0, 0, 5476, -607836]$	$y^2=x^3+5476x-607836$	518.2.0.?	$[]$
103600.bb1	103600d1	103600.bb	103600d	$1$	$1$	$ 2^{4} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 5^{6} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$41472$	$0.411097$	$27648/259$	$0.75618$	$2.43755$	$[0, 0, 0, 100, 1500]$	$y^2=x^3+100x+1500$	518.2.0.?	$[]$
116032.be1	116032bg1	116032.be	116032bg	$1$	$1$	$ 2^{6} \cdot 7^{2} \cdot 37 $	$ - 2^{14} \cdot 7^{7} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$147456$	$0.925906$	$27648/259$	$0.75618$	$2.94361$	$[0, 0, 0, 784, -32928]$	$y^2=x^3+784x-32928$	518.2.0.?	$[]$
116032.bf1	116032j1	116032.bf	116032j	$1$	$1$	$ 2^{6} \cdot 7^{2} \cdot 37 $	$ - 2^{14} \cdot 7^{7} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$2.884156216$	$1$	$0$	$147456$	$0.925906$	$27648/259$	$0.75618$	$2.94361$	$[0, 0, 0, 784, 32928]$	$y^2=x^3+784x+32928$	518.2.0.?	$[(-7/2, 1421/2)]$
130536.co1	130536w1	130536.co	130536w	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{7} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$294912$	$1.128639$	$27648/259$	$0.75618$	$3.12071$	$[0, 0, 0, 1764, -111132]$	$y^2=x^3+1764x-111132$	518.2.0.?	$[]$
149184.gh1	149184gb1	149184.gh	149184gb	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 3^{6} \cdot 7 \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$3.991836159$	$1$	$2$	$98304$	$0.502257$	$27648/259$	$0.75618$	$2.45477$	$[0, 0, 0, 144, 2592]$	$y^2=x^3+144x+2592$	518.2.0.?	$[(153, 1899)]$
149184.go1	149184cu1	149184.go	149184cu	$1$	$1$	$ 2^{6} \cdot 3^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 3^{6} \cdot 7 \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$7.872521675$	$1$	$0$	$98304$	$0.502257$	$27648/259$	$0.75618$	$2.45477$	$[0, 0, 0, 144, -2592]$	$y^2=x^3+144x-2592$	518.2.0.?	$[(6777/11, 566523/11)]$
153328.j1	153328m1	153328.j	153328m	$1$	$1$	$ 2^{4} \cdot 7 \cdot 37^{2} $	$ - 2^{8} \cdot 7 \cdot 37^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$525312$	$1.411837$	$27648/259$	$0.75618$	$3.36326$	$[0, 0, 0, 5476, 607836]$	$y^2=x^3+5476x+607836$	518.2.0.?	$[]$
250712.l1	250712l1	250712.l	250712l	$1$	$1$	$ 2^{3} \cdot 7 \cdot 11^{2} \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 11^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$259200$	$0.805326$	$27648/259$	$0.75618$	$2.64480$	$[0, 0, 0, 484, 15972]$	$y^2=x^3+484x+15972$	518.2.0.?	$[]$
261072.fu1	261072fu1	261072.fu	261072fu	$1$	$1$	$ 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 7^{7} \cdot 37 $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$5.234863911$	$1$	$0$	$589824$	$1.128639$	$27648/259$	$0.75618$	$2.94728$	$[0, 0, 0, 1764, 111132]$	$y^2=x^3+1764x+111132$	518.2.0.?	$[(2961/5, 175959/5)]$
350168.b1	350168b1	350168.b	350168b	$1$	$1$	$ 2^{3} \cdot 7 \cdot 13^{2} \cdot 37 $	$ - 2^{8} \cdot 7 \cdot 13^{6} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$393984$	$0.888852$	$27648/259$	$0.75618$	$2.65410$	$[0, 0, 0, 676, -26364]$	$y^2=x^3+676x-26364$	518.2.0.?	$[]$
362600.bo1	362600bo1	362600.bo	362600bo	$1$	$1$	$ 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 37 $	$ - 2^{8} \cdot 5^{6} \cdot 7^{7} \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$995328$	$1.384052$	$27648/259$	$0.75618$	$3.11108$	$[0, 0, 0, 4900, 514500]$	$y^2=x^3+4900x+514500$	518.2.0.?	$[]$
414400.co1	414400co1	414400.co	414400co	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 5^{6} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$331776$	$0.757670$	$27648/259$	$0.75618$	$2.49784$	$[0, 0, 0, 400, 12000]$	$y^2=x^3+400x+12000$	518.2.0.?	$[]$
414400.dh1	414400dh1	414400.dh	414400dh	$1$	$1$	$ 2^{6} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{14} \cdot 5^{6} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$331776$	$0.757670$	$27648/259$	$0.75618$	$2.49784$	$[0, 0, 0, 400, -12000]$	$y^2=x^3+400x-12000$	518.2.0.?	$[]$
466200.ei1	466200ei1	466200.ei	466200ei	$1$	$1$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 37 $	$ - 2^{8} \cdot 3^{6} \cdot 5^{6} \cdot 7 \cdot 37 $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	$518$	$2$	$0$	$1$	$1$	$0$	$663552$	$0.960402$	$27648/259$	$0.75618$	$2.66168$	$[0, 0, 0, 900, 40500]$	$y^2=x^3+900x+40500$	518.2.0.?	$[]$

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Elliptic 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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