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	Manin constant

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Results (22 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	$Ш_{\textrm{an}}$	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
9240.i3	9240d2	9240.i	9240d	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$6144$	$0.657900$	$73682642884/12006225$	$0.86655$	$3.49945$	$[0, -1, 0, -880, -8228]$	$y^2=x^3-x^2-880x-8228$	2.6.0.a.1, 20.12.0-2.a.1.1, 44.12.0-2.a.1.1, 56.12.0-2.a.1.1, 220.24.0.?, $\ldots$	$[ ]$
18480.dg3	18480bh2	18480.dg	18480bh	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$0.712520357$	$1$	$15$	$12288$	$0.657900$	$73682642884/12006225$	$0.86655$	$3.25255$	$[0, 1, 0, -880, 8228]$	$y^2=x^3+x^2-880x+8228$	2.6.0.a.1, 20.12.0-2.a.1.1, 44.12.0-2.a.1.1, 56.12.0-2.a.1.1, 220.24.0.?, $\ldots$	$[(8, 42)]$
27720.k3	27720bd2	27720.k	27720bd	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$49152$	$1.207205$	$73682642884/12006225$	$0.86655$	$3.76799$	$[0, 0, 0, -7923, 230078]$	$y^2=x^3-7923x+230078$	2.6.0.a.1, 60.12.0-2.a.1.1, 132.12.0.?, 168.12.0.?, 220.12.0.?, $\ldots$	$[ ]$
46200.ct3	46200cv2	46200.ct	46200cv	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$147456$	$1.462618$	$73682642884/12006225$	$0.86655$	$3.87414$	$[0, 1, 0, -22008, -1072512]$	$y^2=x^3+x^2-22008x-1072512$	2.6.0.a.1, 4.12.0-2.a.1.1, 220.24.0.?, 280.24.0.?, 616.24.0.?, $\ldots$	$[ ]$
55440.bt3	55440p2	55440.bt	55440p	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1.401266006$	$1$	$13$	$98304$	$1.207205$	$73682642884/12006225$	$0.86655$	$3.52888$	$[0, 0, 0, -7923, -230078]$	$y^2=x^3-7923x-230078$	2.6.0.a.1, 60.12.0-2.a.1.1, 132.12.0.?, 168.12.0.?, 220.12.0.?, $\ldots$	$[(-61, 162)]$
64680.bv3	64680q2	64680.bv	64680q	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$1.736180446$	$1$	$9$	$294912$	$1.630856$	$73682642884/12006225$	$0.86655$	$3.93872$	$[0, 1, 0, -43136, 2908464]$	$y^2=x^3+x^2-43136x+2908464$	2.6.0.a.1, 8.12.0-2.a.1.1, 140.12.0.?, 220.12.0.?, 280.24.0.?, $\ldots$	$[(-68, 2352)]$
73920.bf3	73920er2	73920.bf	73920er	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$1.416677212$	$1$	$11$	$98304$	$1.004473$	$73682642884/12006225$	$0.86655$	$3.22132$	$[0, -1, 0, -3521, 69345]$	$y^2=x^3-x^2-3521x+69345$	2.6.0.a.1, 28.12.0-2.a.1.1, 40.12.0-2.a.1.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[(59, 252)]$
73920.ez3	73920ch2	73920.ez	73920ch	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$1.270246685$	$1$	$11$	$98304$	$1.004473$	$73682642884/12006225$	$0.86655$	$3.22132$	$[0, 1, 0, -3521, -69345]$	$y^2=x^3+x^2-3521x-69345$	2.6.0.a.1, 28.12.0-2.a.1.1, 40.12.0-2.a.1.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[(-29, 96)]$
92400.ba3	92400i2	92400.ba	92400i	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$2.200276564$	$1$	$29$	$294912$	$1.462618$	$73682642884/12006225$	$0.86655$	$3.63928$	$[0, -1, 0, -22008, 1072512]$	$y^2=x^3-x^2-22008x+1072512$	2.6.0.a.1, 4.12.0-2.a.1.1, 220.24.0.?, 280.24.0.?, 616.24.0.?, $\ldots$	$[(12, 900), (462, 9450)]$
101640.bd3	101640cc2	101640.bd	101640cc	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$4.333701707$	$1$	$5$	$737280$	$1.856848$	$73682642884/12006225$	$0.86655$	$4.01952$	$[0, -1, 0, -106520, 11377500]$	$y^2=x^3-x^2-106520x+11377500$	2.6.0.a.1, 4.12.0-2.a.1.1, 220.24.0.?, 280.24.0.?, 616.24.0.?, $\ldots$	$[(1646, 65520)]$
129360.bo3	129360ba2	129360.bo	129360ba	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$2.171192366$	$1$	$9$	$589824$	$1.630856$	$73682642884/12006225$	$0.86655$	$3.70677$	$[0, -1, 0, -43136, -2908464]$	$y^2=x^3-x^2-43136x-2908464$	2.6.0.a.1, 8.12.0-2.a.1.1, 140.12.0.?, 220.12.0.?, 280.24.0.?, $\ldots$	$[(-124, 720)]$
138600.ec3	138600dl2	138600.ec	138600dl	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$1179648$	$2.011925$	$73682642884/12006225$	$0.86655$	$4.07141$	$[0, 0, 0, -198075, 28759750]$	$y^2=x^3-198075x+28759750$	2.6.0.a.1, 12.12.0-2.a.1.1, 220.12.0.?, 280.12.0.?, 616.12.0.?, $\ldots$	$[ ]$
194040.ei3	194040d2	194040.ei	194040d	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$2359296$	$2.180161$	$73682642884/12006225$	$0.86655$	$4.12470$	$[0, 0, 0, -388227, -78916754]$	$y^2=x^3-388227x-78916754$	2.6.0.a.1, 24.12.0-2.a.1.1, 220.12.0.?, 280.12.0.?, 420.12.0.?, $\ldots$	$[ ]$
203280.ft3	203280fd2	203280.ft	203280fd	$4$	$4$	$ 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.1	2Cs	$3080$	$48$	$0$	$1$	$1$	$3$	$1474560$	$1.856848$	$73682642884/12006225$	$0.86655$	$3.79157$	$[0, 1, 0, -106520, -11377500]$	$y^2=x^3+x^2-106520x-11377500$	2.6.0.a.1, 4.12.0-2.a.1.1, 220.24.0.?, 280.24.0.?, 616.24.0.?, $\ldots$	$[ ]$
221760.gx3	221760ju2	221760.gx	221760ju	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1.609337184$	$1$	$11$	$786432$	$1.553780$	$73682642884/12006225$	$0.86655$	$3.46932$	$[0, 0, 0, -31692, 1840624]$	$y^2=x^3-31692x+1840624$	2.6.0.a.1, 84.12.0.?, 120.12.0.?, 220.12.0.?, 264.12.0.?, $\ldots$	$[(8, 1260)]$
221760.my3	221760f2	221760.my	221760f	$4$	$4$	$ 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$786432$	$1.553780$	$73682642884/12006225$	$0.86655$	$3.46932$	$[0, 0, 0, -31692, -1840624]$	$y^2=x^3-31692x-1840624$	2.6.0.a.1, 84.12.0.?, 120.12.0.?, 220.12.0.?, 264.12.0.?, $\ldots$	$[ ]$
277200.t3	277200t2	277200.t	277200t	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$2$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$3.715723925$	$1$	$29$	$2359296$	$2.011925$	$73682642884/12006225$	$0.86655$	$3.84623$	$[0, 0, 0, -198075, -28759750]$	$y^2=x^3-198075x-28759750$	2.6.0.a.1, 12.12.0-2.a.1.1, 220.12.0.?, 280.12.0.?, 616.12.0.?, $\ldots$	$[(-251, 2268), (721, 14256)]$
304920.bt3	304920bt2	304920.bt	304920bt	$4$	$4$	$ 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11^{2} $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{2} \cdot 11^{8} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$5898240$	$2.406155$	$73682642884/12006225$	$0.86655$	$4.19183$	$[0, 0, 0, -958683, -306233818]$	$y^2=x^3-958683x-306233818$	2.6.0.a.1, 12.12.0-2.a.1.1, 220.12.0.?, 280.12.0.?, 616.12.0.?, $\ldots$	$[ ]$
323400.bj3	323400bj2	323400.bj	323400bj	$4$	$4$	$ 2^{3} \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{4} \cdot 5^{8} \cdot 7^{8} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$3080$	$48$	$0$	$2.754809083$	$1$	$9$	$7077888$	$2.435574$	$73682642884/12006225$	$0.86655$	$4.20021$	$[0, -1, 0, -1078408, 365714812]$	$y^2=x^3-x^2-1078408x+365714812$	2.6.0.a.1, 28.12.0-2.a.1.1, 40.12.0-2.a.1.1, 88.12.0.?, 220.12.0.?, $\ldots$	$[(838, 7056)]$
369600.lc3	369600lc2	369600.lc	369600lc	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$3.678298625$	$1$	$7$	$2359296$	$1.809193$	$73682642884/12006225$	$0.86655$	$3.57015$	$[0, -1, 0, -88033, -8492063]$	$y^2=x^3-x^2-88033x-8492063$	2.6.0.a.1, 8.12.0-2.a.1.1, 140.12.0.?, 220.12.0.?, 280.24.0.?, $\ldots$	$[(463, 7056)]$
369600.nr3	369600nr2	369600.nr	369600nr	$4$	$4$	$ 2^{6} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 11 $	$ 2^{16} \cdot 3^{4} \cdot 5^{8} \cdot 7^{2} \cdot 11^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.1	2Cs	$3080$	$48$	$0$	$1.851027274$	$1$	$9$	$2359296$	$1.809193$	$73682642884/12006225$	$0.86655$	$3.57015$	$[0, 1, 0, -88033, 8492063]$	$y^2=x^3+x^2-88033x+8492063$	2.6.0.a.1, 8.12.0-2.a.1.1, 140.12.0.?, 220.12.0.?, 280.24.0.?, $\ldots$	$[(47, 2112)]$
388080.iq3	388080iq2	388080.iq	388080iq	$4$	$4$	$ 2^{4} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 11 $	$ 2^{10} \cdot 3^{10} \cdot 5^{2} \cdot 7^{8} \cdot 11^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	2.6.0.1	2Cs	$9240$	$48$	$0$	$1$	$1$	$3$	$4718592$	$2.180161$	$73682642884/12006225$	$0.86655$	$3.90254$	$[0, 0, 0, -388227, 78916754]$	$y^2=x^3-388227x+78916754$	2.6.0.a.1, 24.12.0-2.a.1.1, 220.12.0.?, 280.12.0.?, 420.12.0.?, $\ldots$	$[ ]$

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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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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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