LMFDB - Elliptic curves over $\Q$ of conductor 320

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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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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
320.a1	320f3	320.a	320f	$4$	$6$	$ 2^{6} \cdot 5 $	$ 2^{10} \cdot 5^{3} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.21, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$0.275624609$	$1$	$9$	$48$	$-0.034070$	$488095744/125$	$1.07376$	$4.66990$	$[0, 1, 0, -165, 763]$	$y^2=x^3+x^2-165x+763$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 8.12.0-4.b.1.3, $\ldots$	$[(6, 5)]$
320.a2	320f4	320.a	320f	$4$	$6$	$ 2^{6} \cdot 5 $	$ - 2^{14} \cdot 5^{6} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.12.0.12, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$0.137812304$	$1$	$15$	$96$	$0.312503$	$-20720464/15625$	$0.95894$	$4.74747$	$[0, 1, 0, -145, 975]$	$y^2=x^3+x^2-145x+975$	2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.a.1.1, 6.12.0.a.1, 12.48.0-12.d.1.1, $\ldots$	$[(-5, 40)]$
320.a3	320f1	320.a	320f	$4$	$6$	$ 2^{6} \cdot 5 $	$ 2^{10} \cdot 5 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.21, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$0.826873828$	$1$	$5$	$16$	$-0.583377$	$16384/5$	$0.95621$	$2.88395$	$[0, 1, 0, -5, -5]$	$y^2=x^3+x^2-5x-5$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 8.12.0-4.b.1.3, $\ldots$	$[(3, 4)]$
320.a4	320f2	320.a	320f	$4$	$6$	$ 2^{6} \cdot 5 $	$ - 2^{14} \cdot 5^{2} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.12.0.12, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$0.413436914$	$1$	$11$	$32$	$-0.236803$	$21296/25$	$0.83964$	$3.41494$	$[0, 1, 0, 15, -17]$	$y^2=x^3+x^2+15x-17$	2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.a.1.1, 6.12.0.a.1, 12.48.0-12.d.1.1, $\ldots$	$[(3, 8)]$
320.b1	320e2	320.b	320e	$2$	$2$	$ 2^{6} \cdot 5 $	$ 2^{12} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$40$	$48$	$0$	$1$	$1$	$1$	$32$	$-0.359471$	$438976/5$	$0.87813$	$3.69431$	$[0, 1, 0, -25, -57]$	$y^2=x^3+x^2-25x-57$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 10.6.0.a.1, 20.12.0.e.1, $\ldots$	$[]$
320.b2	320e1	320.b	320e	$2$	$2$	$ 2^{6} \cdot 5 $	$ - 2^{6} \cdot 5^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.12	2B	$40$	$48$	$0$	$1$	$1$	$1$	$16$	$-0.706045$	$-64/25$	$1.09219$	$2.57163$	$[0, 1, 0, 0, -2]$	$y^2=x^3+x^2-2$	2.3.0.a.1, 4.12.0-4.a.1.1, 20.24.0-20.d.1.1, 40.48.0-40.t.1.1	$[]$
320.c1	320b3	320.c	320b	$4$	$4$	$ 2^{6} \cdot 5 $	$ 2^{16} \cdot 5 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.216	2B	$80$	$192$	$3$	$2.888821352$	$1$	$3$	$64$	$0.144360$	$132304644/5$	$1.13632$	$5.16458$	$[0, 0, 0, -428, -3408]$	$y^2=x^3-428x-3408$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.o.1.5, 10.6.0.a.1, 16.48.0-16.i.1.5, $\ldots$	$[(24, 12)]$
320.c2	320b2	320.c	320b	$4$	$4$	$ 2^{6} \cdot 5 $	$ 2^{14} \cdot 5^{2} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.156	2Cs	$40$	$192$	$3$	$1.444410676$	$1$	$11$	$32$	$-0.202214$	$148176/25$	$1.09175$	$3.74636$	$[0, 0, 0, -28, -48]$	$y^2=x^3-28x-48$	2.6.0.a.1, 4.12.0.a.1, 8.48.0-8.g.1.2, 20.24.0.b.1, 40.192.3-40.bk.1.6	$[(-3, 3)]$
320.c3	320b1	320.c	320b	$4$	$4$	$ 2^{6} \cdot 5 $	$ 2^{10} \cdot 5 $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.220	2B	$80$	$192$	$3$	$0.722205338$	$1$	$5$	$16$	$-0.548787$	$55296/5$	$1.01898$	$3.09482$	$[0, 0, 0, -8, 8]$	$y^2=x^3-8x+8$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.o.1.7, 10.6.0.a.1, 16.48.0-16.i.1.7, $\ldots$	$[(1, 1)]$
320.c4	320b4	320.c	320b	$4$	$4$	$ 2^{6} \cdot 5 $	$ - 2^{16} \cdot 5^{4} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.4	2B	$80$	$192$	$3$	$0.722205338$	$1$	$7$	$64$	$0.144360$	$237276/625$	$1.04671$	$4.28803$	$[0, 0, 0, 52, -272]$	$y^2=x^3+52x-272$	2.3.0.a.1, 4.24.0.c.1, 8.48.0-4.c.1.1, 40.96.1-40.dk.1.4, 80.192.3.?	$[(6, 16)]$
320.d1	320a3	320.d	320a	$4$	$4$	$ 2^{6} \cdot 5 $	$ 2^{16} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.220	2B	$80$	$192$	$3$	$1$	$1$	$1$	$64$	$0.144360$	$132304644/5$	$1.13632$	$5.16458$	$[0, 0, 0, -428, 3408]$	$y^2=x^3-428x+3408$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.o.1.7, 10.6.0.a.1, 16.48.0-16.i.1.7, $\ldots$	$[]$
320.d2	320a2	320.d	320a	$4$	$4$	$ 2^{6} \cdot 5 $	$ 2^{14} \cdot 5^{2} $	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.156	2Cs	$40$	$192$	$3$	$1$	$1$	$3$	$32$	$-0.202214$	$148176/25$	$1.09175$	$3.74636$	$[0, 0, 0, -28, 48]$	$y^2=x^3-28x+48$	2.6.0.a.1, 4.12.0.a.1, 8.48.0-8.g.1.2, 20.24.0.b.1, 40.192.3-40.bk.1.2	$[]$
320.d3	320a1	320.d	320a	$4$	$4$	$ 2^{6} \cdot 5 $	$ 2^{10} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	16.48.0.216	2B	$80$	$192$	$3$	$1$	$1$	$1$	$16$	$-0.548787$	$55296/5$	$1.01898$	$3.09482$	$[0, 0, 0, -8, -8]$	$y^2=x^3-8x-8$	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.o.1.5, 10.6.0.a.1, 16.48.0-16.i.1.5, $\ldots$	$[]$
320.d4	320a4	320.d	320a	$4$	$4$	$ 2^{6} \cdot 5 $	$ - 2^{16} \cdot 5^{4} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.48.0.4	2B	$80$	$192$	$3$	$1$	$1$	$1$	$64$	$0.144360$	$237276/625$	$1.04671$	$4.28803$	$[0, 0, 0, 52, 272]$	$y^2=x^3+52x+272$	2.3.0.a.1, 4.24.0.c.1, 8.48.0-4.c.1.1, 40.96.1-40.dk.1.4, 80.192.3.?	$[]$
320.e1	320d2	320.e	320d	$2$	$2$	$ 2^{6} \cdot 5 $	$ 2^{12} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	8.12.0.21	2B	$40$	$48$	$0$	$1$	$1$	$1$	$32$	$-0.359471$	$438976/5$	$0.87813$	$3.69431$	$[0, -1, 0, -25, 57]$	$y^2=x^3-x^2-25x+57$	2.3.0.a.1, 4.6.0.b.1, 8.12.0-4.b.1.3, 10.6.0.a.1, 20.12.0.e.1, $\ldots$	$[]$
320.e2	320d1	320.e	320d	$2$	$2$	$ 2^{6} \cdot 5 $	$ - 2^{6} \cdot 5^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2$	4.12.0.12	2B	$40$	$48$	$0$	$1$	$1$	$1$	$16$	$-0.706045$	$-64/25$	$1.09219$	$2.57163$	$[0, -1, 0, 0, 2]$	$y^2=x^3-x^2+2$	2.3.0.a.1, 4.12.0-4.a.1.1, 20.24.0-20.d.1.1, 40.48.0-40.t.1.6	$[]$
320.f1	320c3	320.f	320c	$4$	$6$	$ 2^{6} \cdot 5 $	$ 2^{10} \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.21, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$48$	$-0.034070$	$488095744/125$	$1.07376$	$4.66990$	$[0, -1, 0, -165, -763]$	$y^2=x^3-x^2-165x-763$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 8.12.0-4.b.1.3, $\ldots$	$[]$
320.f2	320c4	320.f	320c	$4$	$6$	$ 2^{6} \cdot 5 $	$ - 2^{14} \cdot 5^{6} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.12.0.12, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$96$	$0.312503$	$-20720464/15625$	$0.95894$	$4.74747$	$[0, -1, 0, -145, -975]$	$y^2=x^3-x^2-145x-975$	2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.a.1.1, 6.12.0.a.1, 12.48.0-12.d.1.1, $\ldots$	$[]$
320.f3	320c1	320.f	320c	$4$	$6$	$ 2^{6} \cdot 5 $	$ 2^{10} \cdot 5 $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	8.12.0.21, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$16$	$-0.583377$	$16384/5$	$0.95621$	$2.88395$	$[0, -1, 0, -5, 5]$	$y^2=x^3-x^2-5x+5$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.b.1, 6.12.0.a.1, 8.12.0-4.b.1.3, $\ldots$	$[]$
320.f4	320c2	320.f	320c	$4$	$6$	$ 2^{6} \cdot 5 $	$ - 2^{14} \cdot 5^{2} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	$2, 3$	4.12.0.12, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$32$	$-0.236803$	$21296/25$	$0.83964$	$3.41494$	$[0, -1, 0, 15, 17]$	$y^2=x^3-x^2+15x+17$	2.3.0.a.1, 3.4.0.a.1, 4.12.0-4.a.1.1, 6.12.0.a.1, 12.48.0-12.d.1.1, $\ldots$	$[]$

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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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