LMFDB - Elliptic curves over $\Q$ of conductor 400

The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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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	Potentially good	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	Manin constant
400.a1	400h1	400.a	400h	$1$	$1$	$ 2^{4} \cdot 5^{2} $	$ - 2^{11} \cdot 5^{2} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.2.0.1		$8$	$2$	$0$	$0.128375062$	$1$	$8$	$48$	$-0.413520$	$270$	$1.01898$	$3.02569$	$[0, 0, 0, 5, 10]$	$y^2=x^3+5x+10$	8.2.0.a.1	$[(1, 4)]$	$1$
400.b1	400f2	400.b	400f	$2$	$2$	$ 2^{4} \cdot 5^{2} $	$ 2^{8} \cdot 5^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	16.96.3.346	2B	$80$	$384$	$9$	$1$	$1$	$1$	$160$	$0.478073$	$78608$	$0.87912$	$5.22449$	$[0, 1, 0, -708, -7412]$	$y^2=x^3+x^2-708x-7412$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 10.6.0.a.1, 16.96.3.ey.1, $\ldots$	$[ ]$	$1$
400.b2	400f1	400.b	400f	$2$	$2$	$ 2^{4} \cdot 5^{2} $	$ 2^{4} \cdot 5^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	16.96.3.338	2B	$80$	$384$	$9$	$1$	$1$	$1$	$80$	$0.131500$	$2048$	$1.01898$	$4.15293$	$[0, 1, 0, -83, 88]$	$y^2=x^3+x^2-83x+88$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.1, 10.6.0.a.1, 16.96.3.ey.2, $\ldots$	$[ ]$	$1$
400.c1	400e3	400.c	400e	$4$	$6$	$ 2^{4} \cdot 5^{2} $	$ 2^{4} \cdot 5^{9} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	8.12.0.24, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$144$	$0.424075$	$488095744/125$	$1.07376$	$5.41357$	$[0, 1, 0, -1033, 12438]$	$y^2=x^3+x^2-1033x+12438$	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.1.4, $\ldots$	$[ ]$	$1$
400.c2	400e4	400.c	400e	$4$	$6$	$ 2^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 5^{12} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	8.12.0.38, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$288$	$0.770649$	$-20720464/15625$	$0.95894$	$5.48825$	$[0, 1, 0, -908, 15688]$	$y^2=x^3+x^2-908x+15688$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 8.12.0-4.a.1.2, $\ldots$	$[ ]$	$1$
400.c3	400e1	400.c	400e	$4$	$6$	$ 2^{4} \cdot 5^{2} $	$ 2^{4} \cdot 5^{7} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	8.12.0.24, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$48$	$-0.125231$	$16384/5$	$0.95621$	$3.69413$	$[0, 1, 0, -33, -62]$	$y^2=x^3+x^2-33x-62$	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.1.4, $\ldots$	$[ ]$	$1$
400.c4	400e2	400.c	400e	$4$	$6$	$ 2^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 5^{8} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2, 3$	8.12.0.38, 3.4.0.1	2B, 3B	$120$	$384$	$9$	$1$	$1$	$1$	$96$	$0.221343$	$21296/25$	$0.83964$	$4.20535$	$[0, 1, 0, 92, -312]$	$y^2=x^3+x^2+92x-312$	2.3.0.a.1, 3.4.0.a.1, 4.6.0.a.1, 6.12.0.a.1, 8.12.0-4.a.1.2, $\ldots$	$[ ]$	$1$
400.d1	400c2	400.d	400c	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{15} \cdot 5^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.2	3B, 5B.4.2	$120$	$384$	$9$	$0.194697629$	$1$	$8$	$144$	$0.516354$	$-349938025/8$	$1.05078$	$5.74631$	$[0, -1, 0, -2008, 35312]$	$y^2=x^3-x^2-2008x+35312$	3.4.0.a.1, 5.12.0.a.2, 8.2.0.a.1, 12.8.0-3.a.1.2, 15.96.1.a.1, $\ldots$	$[(28, 16)]$	$1$
400.d2	400c3	400.d	400c	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{17} \cdot 5^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.1	3B, 5B.4.1	$120$	$384$	$9$	$0.324496049$	$1$	$8$	$240$	$0.771767$	$-121945/32$	$0.94334$	$5.55432$	$[0, -1, 0, -1208, -19088]$	$y^2=x^3-x^2-1208x-19088$	3.4.0.a.1, 5.12.0.a.1, 8.2.0.a.1, 12.8.0-3.a.1.1, 15.96.1.a.4, $\ldots$	$[(92, 800)]$	$1$
400.d3	400c1	400.d	400c	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{13} \cdot 5^{4} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.2	3B, 5B.4.2	$120$	$384$	$9$	$0.064899209$	$1$	$12$	$48$	$-0.032952$	$-25/2$	$1.09044$	$3.82387$	$[0, -1, 0, -8, 112]$	$y^2=x^3-x^2-8x+112$	3.4.0.a.1, 5.12.0.a.2, 8.2.0.a.1, 12.8.0-3.a.1.1, 15.96.1.a.2, $\ldots$	$[(12, 40)]$	$1$
400.d4	400c4	400.d	400c	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{27} \cdot 5^{8} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.1	3B, 5B.4.1	$120$	$384$	$9$	$0.973488147$	$1$	$4$	$720$	$1.321074$	$46969655/32768$	$1.06296$	$6.48561$	$[0, -1, 0, 8792, 140912]$	$y^2=x^3-x^2+8792x+140912$	3.4.0.a.1, 5.12.0.a.1, 8.2.0.a.1, 12.8.0-3.a.1.2, 15.96.1.a.3, $\ldots$	$[(68, 1024)]$	$1$
400.e1	400a3	400.e	400a	$4$	$4$	$ 2^{4} \cdot 5^{2} $	$ 2^{10} \cdot 5^{7} $	$1$	$\Z/4\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.48.0.41	2B	$80$	$192$	$3$	$0.933393502$	$1$	$11$	$192$	$0.602505$	$132304644/5$	$1.13632$	$5.88983$	$[0, 0, 0, -2675, 53250]$	$y^2=x^3-2675x+53250$	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.o.1.8, 10.6.0.a.1, 16.48.0-16.i.1.8, $\ldots$	$[(29, 8)]$	$1$
400.e2	400a2	400.e	400a	$4$	$4$	$ 2^{4} \cdot 5^{2} $	$ 2^{8} \cdot 5^{8} $	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.22	2Cs	$40$	$192$	$3$	$1.866787005$	$1$	$7$	$96$	$0.255931$	$148176/25$	$1.09175$	$4.52443$	$[0, 0, 0, -175, 750]$	$y^2=x^3-175x+750$	2.6.0.a.1, 4.24.0-4.a.1.2, 8.48.0-8.g.1.4, 20.48.0-20.b.1.2, 40.192.3-40.bk.1.8	$[(1, 24)]$	$1$
400.e3	400a1	400.e	400a	$4$	$4$	$ 2^{4} \cdot 5^{2} $	$ 2^{4} \cdot 5^{7} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	16.48.0.57	2B	$80$	$192$	$3$	$0.933393502$	$1$	$3$	$48$	$-0.090642$	$55296/5$	$1.01898$	$3.89716$	$[0, 0, 0, -50, -125]$	$y^2=x^3-50x-125$	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.o.1.6, 10.6.0.a.1, 16.48.0-16.i.1.6, $\ldots$	$[(15, 50)]$	$1$
400.e4	400a4	400.e	400a	$4$	$4$	$ 2^{4} \cdot 5^{2} $	$ - 2^{10} \cdot 5^{10} $	$1$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$		$2$	8.48.0.5	2B	$80$	$192$	$3$	$0.933393502$	$1$	$7$	$192$	$0.602505$	$237276/625$	$1.04671$	$5.04593$	$[0, 0, 0, 325, 4250]$	$y^2=x^3+325x+4250$	2.3.0.a.1, 4.24.0.c.1, 8.48.0-4.c.1.2, 20.48.0-4.c.1.1, 40.96.1-40.dk.1.2, $\ldots$	$[(-5, 50)]$	$1$
400.f1	400b4	400.f	400b	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{15} \cdot 5^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.2	3B, 5B.4.2	$120$	$384$	$9$	$1$	$1$	$0$	$720$	$1.321074$	$-349938025/8$	$1.05078$	$7.35804$	$[0, 1, 0, -50208, 4313588]$	$y^2=x^3+x^2-50208x+4313588$	3.4.0.a.1, 5.12.0.a.2, 8.2.0.a.1, 15.96.1.a.1, 20.24.0-5.a.2.2, $\ldots$	$[ ]$	$1$
400.f2	400b3	400.f	400b	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{13} \cdot 5^{10} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.2	3B, 5B.4.2	$120$	$384$	$9$	$1$	$1$	$0$	$240$	$0.771767$	$-25/2$	$1.09044$	$5.43560$	$[0, 1, 0, -208, 13588]$	$y^2=x^3+x^2-208x+13588$	3.4.0.a.1, 5.12.0.a.2, 8.2.0.a.1, 15.96.1.a.2, 20.24.0-5.a.2.2, $\ldots$	$[ ]$	$1$
400.f3	400b1	400.f	400b	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{17} \cdot 5^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.1	3B, 5B.4.1	$120$	$384$	$9$	$1$	$1$	$0$	$48$	$-0.032952$	$-121945/32$	$0.94334$	$3.94259$	$[0, 1, 0, -48, -172]$	$y^2=x^3+x^2-48x-172$	3.4.0.a.1, 5.12.0.a.1, 8.2.0.a.1, 15.96.1.a.4, 20.24.0-5.a.1.2, $\ldots$	$[ ]$	$1$
400.f4	400b2	400.f	400b	$4$	$15$	$ 2^{4} \cdot 5^{2} $	$ - 2^{27} \cdot 5^{2} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$2, 3, 5$	8.2.0.1, 3.4.0.1, 5.12.0.1	3B, 5B.4.1	$120$	$384$	$9$	$1$	$1$	$0$	$144$	$0.516354$	$46969655/32768$	$1.06296$	$4.87388$	$[0, 1, 0, 352, 1268]$	$y^2=x^3+x^2+352x+1268$	3.4.0.a.1, 5.12.0.a.1, 8.2.0.a.1, 15.96.1.a.3, 20.24.0-5.a.1.2, $\ldots$	$[ ]$	$1$
400.g1	400d2	400.g	400d	$2$	$2$	$ 2^{4} \cdot 5^{2} $	$ 2^{8} \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	16.96.3.346	2B	$80$	$384$	$9$	$1$	$1$	$1$	$32$	$-0.326646$	$78608$	$0.87912$	$3.61276$	$[0, -1, 0, -28, -48]$	$y^2=x^3-x^2-28x-48$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.2, 10.6.0.a.1, 16.96.3.ey.1, $\ldots$	$[ ]$	$1$
400.g2	400d1	400.g	400d	$2$	$2$	$ 2^{4} \cdot 5^{2} $	$ 2^{4} \cdot 5^{3} $	$0$	$\Z/2\Z$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	16.96.3.338	2B	$80$	$384$	$9$	$1$	$1$	$1$	$16$	$-0.673220$	$2048$	$1.01898$	$2.54120$	$[0, -1, 0, -3, 2]$	$y^2=x^3-x^2-3x+2$	2.3.0.a.1, 4.6.0.d.1, 8.24.0.bl.1, 10.6.0.a.1, 16.96.3.ey.2, $\ldots$	$[ ]$	$1$
400.h1	400g1	400.h	400g	$1$	$1$	$ 2^{4} \cdot 5^{2} $	$ - 2^{11} \cdot 5^{8} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2$	8.2.0.1		$8$	$2$	$0$	$1$	$1$	$0$	$240$	$0.391199$	$270$	$1.01898$	$4.63742$	$[0, 0, 0, 125, 1250]$	$y^2=x^3+125x+1250$	8.2.0.a.1	$[ ]$	$1$

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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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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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