LMFDB - Elliptic curves over $\Q$ of conductor 8100

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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	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
8100.a1	8100f2	8100.a	8100f	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{10} \cdot 5^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3, 5$	4.2.0.1, 3.4.0.1, 5.5.0.1	3B, 5S4	$120$	$160$	$4$	$1$	$1$	$0$	$11664$	$1.049465$	$-316368$	$0.93828$	$4.31774$	$[0, 0, 0, -8775, -317250]$	$y^2=x^3-8775x-317250$	3.4.0.a.1, 4.2.0.a.1, 5.5.0.a.1, 12.8.0.a.1, 15.40.1-15.a.1.1, $\ldots$	$[]$
8100.a2	8100f1	8100.a	8100f	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{6} \cdot 5^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3, 5$	4.2.0.1, 3.4.0.1, 5.5.0.1	3B, 5S4	$120$	$160$	$4$	$1$	$1$	$0$	$3888$	$0.500160$	$432$	$0.77371$	$3.21797$	$[0, 0, 0, 225, -2250]$	$y^2=x^3+225x-2250$	3.4.0.a.1, 4.2.0.a.1, 5.5.0.a.1, 12.8.0.a.1, 15.40.1-15.a.1.2, $\ldots$	$[]$
8100.b1	8100d2	8100.b	8100d	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{12} \cdot 5^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$93312$	$2.083042$	$183711891456/125$	$1.15925$	$6.03601$	$[0, 0, 0, -1522800, -723289500]$	$y^2=x^3-1522800x-723289500$	3.4.0.a.1, 6.8.0-3.a.1.2, 10.2.0.a.1, 15.8.0-3.a.1.1, 30.16.0-30.a.1.2	$[]$
8100.b2	8100d1	8100.b	8100d	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{15} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$31104$	$1.533737$	$4045602816/1953125$	$1.18271$	$4.63543$	$[0, 0, 0, -22800, -539500]$	$y^2=x^3-22800x-539500$	3.4.0.a.1, 6.8.0-3.a.1.1, 10.2.0.a.1, 15.8.0-3.a.1.2, 30.16.0-30.a.1.3	$[]$
8100.c1	8100l1	8100.c	8100l	$1$	$1$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{10} \cdot 5^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$5$	5.5.0.1	5S4	$10$	$30$	$0$	$1.741972502$	$1$	$0$	$17280$	$1.391073$	$73728$	$1.42657$	$4.69180$	$[0, 0, 0, -27000, -1687500]$	$y^2=x^3-27000x-1687500$	5.5.0.a.1, 10.30.0.a.1	$[(-375/2, 1125/2)]$
8100.d1	8100k1	8100.d	8100k	$1$	$1$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$5$	5.5.0.1	5S4	$10$	$30$	$0$	$0.581870822$	$1$	$4$	$5760$	$0.841767$	$73728$	$1.42657$	$3.95936$	$[0, 0, 0, -3000, 62500]$	$y^2=x^3-3000x+62500$	5.5.0.a.1, 10.30.0.a.1	$[(0, 250)]$
8100.e1	8100c2	8100.e	8100c	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{10} \cdot 5^{15} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$93312$	$2.083042$	$4045602816/1953125$	$1.18271$	$5.36787$	$[0, 0, 0, -205200, 14566500]$	$y^2=x^3-205200x+14566500$	3.4.0.a.1, 6.8.0-3.a.1.2, 10.2.0.a.1, 15.8.0-3.a.1.1, 30.16.0-30.a.1.2	$[]$
8100.e2	8100c1	8100.e	8100c	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{6} \cdot 5^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$31104$	$1.533737$	$183711891456/125$	$1.15925$	$5.30357$	$[0, 0, 0, -169200, 26788500]$	$y^2=x^3-169200x+26788500$	3.4.0.a.1, 6.8.0-3.a.1.1, 10.2.0.a.1, 15.8.0-3.a.1.2, 30.16.0-30.a.1.3	$[]$
8100.f1	8100e1	8100.f	8100e	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 5^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3, 5$	4.2.0.1, 3.4.0.1, 5.5.0.1	3B, 5S4	$120$	$160$	$4$	$1$	$1$	$0$	$3888$	$0.500160$	$-316368$	$0.93828$	$3.58530$	$[0, 0, 0, -975, 11750]$	$y^2=x^3-975x+11750$	3.4.0.a.1, 4.2.0.a.1, 5.5.0.a.1, 12.8.0.a.1, 15.40.1-15.a.1.2, $\ldots$	$[]$
8100.f2	8100e2	8100.f	8100e	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{12} \cdot 5^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3, 5$	4.2.0.1, 3.4.0.1, 5.5.0.1	3B, 5S4	$120$	$160$	$4$	$1$	$1$	$0$	$11664$	$1.049465$	$432$	$0.77371$	$3.95041$	$[0, 0, 0, 2025, 60750]$	$y^2=x^3+2025x+60750$	3.4.0.a.1, 4.2.0.a.1, 5.5.0.a.1, 12.8.0.a.1, 15.40.1-15.a.1.1, $\ldots$	$[]$
8100.g1	8100n2	8100.g	8100n	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{4} \cdot 3^{10} \cdot 5^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$180$	$96$	$2$	$0.841192210$	$1$	$4$	$5832$	$0.859673$	$790272$	$0.98305$	$4.11078$	$[0, 0, 0, -4725, -124875]$	$y^2=x^3-4725x-124875$	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 15.8.0-3.a.1.1, $\ldots$	$[(-39, 9)]$
8100.g2	8100n1	8100.g	8100n	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{4} \cdot 3^{6} \cdot 5^{6} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$180$	$96$	$2$	$2.523576631$	$1$	$2$	$1944$	$0.310366$	$6912$	$0.77371$	$3.09590$	$[0, 0, 0, -225, 1125]$	$y^2=x^3-225x+1125$	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.1, 15.8.0-3.a.1.2, $\ldots$	$[(4, 17)]$
8100.h1	8100m1	8100.h	8100m	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{6} \cdot 5^{7} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$60$	$16$	$0$	$1.807755455$	$1$	$2$	$5184$	$0.724242$	$-148176/5$	$0.76106$	$3.75086$	$[0, 0, 0, -1575, 24750]$	$y^2=x^3-1575x+24750$	3.4.0.a.1, 12.8.0-3.a.1.3, 15.8.0-3.a.1.2, 20.2.0.a.1, 60.16.0-60.a.1.7	$[(10, 100)]$
8100.h2	8100m2	8100.h	8100m	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{10} \cdot 5^{9} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$60$	$16$	$0$	$0.602585151$	$1$	$6$	$15552$	$1.273548$	$191664/125$	$0.87436$	$4.26145$	$[0, 0, 0, 7425, 87750]$	$y^2=x^3+7425x+87750$	3.4.0.a.1, 12.8.0-3.a.1.4, 15.8.0-3.a.1.1, 20.2.0.a.1, 60.16.0-60.a.1.6	$[(15, 450)]$
8100.i1	8100a2	8100.i	8100a	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{12} \cdot 5^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$60$	$16$	$0$	$1$	$1$	$0$	$15552$	$1.273548$	$-148176/5$	$0.76106$	$4.48330$	$[0, 0, 0, -14175, -668250]$	$y^2=x^3-14175x-668250$	3.4.0.a.1, 12.8.0-3.a.1.4, 15.8.0-3.a.1.1, 20.2.0.a.1, 60.16.0-60.a.1.6	$[]$
8100.i2	8100a1	8100.i	8100a	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ - 2^{8} \cdot 3^{4} \cdot 5^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$60$	$16$	$0$	$1$	$1$	$0$	$5184$	$0.724242$	$191664/125$	$0.87436$	$3.52901$	$[0, 0, 0, 825, -3250]$	$y^2=x^3+825x-3250$	3.4.0.a.1, 12.8.0-3.a.1.3, 15.8.0-3.a.1.2, 20.2.0.a.1, 60.16.0-60.a.1.7	$[]$
8100.j1	8100b2	8100.j	8100b	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{4} \cdot 3^{12} \cdot 5^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$180$	$96$	$2$	$1$	$1$	$0$	$5832$	$0.859673$	$6912$	$0.77371$	$3.82834$	$[0, 0, 0, -2025, -30375]$	$y^2=x^3-2025x-30375$	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.1, 15.8.0-3.a.1.1, $\ldots$	$[]$
8100.j2	8100b1	8100.j	8100b	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{4} \cdot 3^{4} \cdot 5^{6} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$180$	$96$	$2$	$1$	$1$	$0$	$1944$	$0.310366$	$790272$	$0.98305$	$3.37834$	$[0, 0, 0, -525, 4625]$	$y^2=x^3-525x+4625$	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 12.16.0.a.2, 15.8.0-3.a.1.2, $\ldots$	$[]$
8100.k1	8100j1	8100.k	8100j	$1$	$1$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{10} \cdot 5^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$5$	5.5.0.1	5S4	$10$	$30$	$0$	$0.907232866$	$1$	$4$	$3456$	$0.586354$	$73728$	$1.42657$	$3.61879$	$[0, 0, 0, -1080, -13500]$	$y^2=x^3-1080x-13500$	5.5.0.a.1, 10.30.0.a.1	$[(-20, 10)]$
8100.l1	8100i1	8100.l	8100i	$1$	$1$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{3} $	$1$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$	✓	$5$	5.5.0.1	5S4	$10$	$30$	$0$	$0.896847520$	$1$	$2$	$1152$	$0.037048$	$73728$	$1.42657$	$2.88635$	$[0, 0, 0, -120, 500]$	$y^2=x^3-120x+500$	5.5.0.a.1, 10.30.0.a.1	$[(5, 5)]$
8100.m1	8100h2	8100.m	8100h	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{12} \cdot 5^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$31104$	$1.457792$	$221184/125$	$1.42657$	$4.52151$	$[0, 0, 0, -16200, -121500]$	$y^2=x^3-16200x-121500$	3.4.0.a.1, 6.8.0-3.a.1.2, 10.2.0.a.1, 15.8.0-3.a.1.1, 30.16.0-30.a.1.2	$[]$
8100.m2	8100h1	8100.m	8100h	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{4} \cdot 5^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$10368$	$0.908486$	$362225664/5$	$1.03419$	$4.36730$	$[0, 0, 0, -10200, 396500]$	$y^2=x^3-10200x+396500$	3.4.0.a.1, 6.8.0-3.a.1.1, 10.2.0.a.1, 15.8.0-3.a.1.2, 30.16.0-30.a.1.3	$[]$
8100.n1	8100g2	8100.n	8100g	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{10} \cdot 5^{7} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$31104$	$1.457792$	$362225664/5$	$1.03419$	$5.09974$	$[0, 0, 0, -91800, -10705500]$	$y^2=x^3-91800x-10705500$	3.4.0.a.1, 6.8.0-3.a.1.2, 10.2.0.a.1, 15.8.0-3.a.1.1, 30.16.0-30.a.1.2	$[]$
8100.n2	8100g1	8100.n	8100g	$2$	$3$	$ 2^{2} \cdot 3^{4} \cdot 5^{2} $	$ 2^{8} \cdot 3^{6} \cdot 5^{9} $	$0$	$\mathsf{trivial}$	$\Q$	$\mathrm{SU}(2)$		$3$	3.4.0.1	3B	$30$	$16$	$0$	$1$	$1$	$0$	$10368$	$0.908486$	$221184/125$	$1.42657$	$3.78907$	$[0, 0, 0, -1800, 4500]$	$y^2=x^3-1800x+4500$	3.4.0.a.1, 6.8.0-3.a.1.1, 10.2.0.a.1, 15.8.0-3.a.1.2, 30.16.0-30.a.1.3	$[]$

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Elliptic curves over $\Q$
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Genus 2 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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