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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (28 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5580.2.a.a	$5580$	$2$	5580.a	1.a	$1$	$1$	$1$	$44.557$	$\Q$	None	✓				620.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-2q^{11}+2q^{13}+3q^{17}+\cdots$
5580.2.a.b	$5580$	$2$	5580.a	1.a	$1$	$1$	$1$	$44.557$	$\Q$	None	✓				1860.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+4q^{11}-4q^{13}+q^{25}+\cdots$
5580.2.a.c	$5580$	$2$	5580.a	1.a	$1$	$1$	$1$	$44.557$	$\Q$	None	✓				620.2.a.b	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+4q^{11}-4q^{13}+4q^{23}+\cdots$
5580.2.a.d	$5580$	$2$	5580.a	1.a	$1$	$1$	$1$	$44.557$	$\Q$	None	✓				1860.2.a.a	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{13}+4q^{17}-4q^{19}-4q^{23}+\cdots$
5580.2.a.e	$5580$	$2$	5580.a	1.a	$1$	$1$	$1$	$44.557$	$\Q$	None	✓				1860.2.a.c	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+4q^{11}+4q^{13}-4q^{17}+\cdots$
5580.2.a.f	$5580$	$2$	5580.a	1.a	$1$	$1$	$1$	$44.557$	$\Q$	None	✓				620.2.a.c	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+2q^{13}+3q^{17}-7q^{19}+\cdots$
5580.2.a.g	$5580$	$2$	5580.a	1.a	$1$	$2$	$2$	$44.557$	$\Q(\sqrt{6}) $	None	✓				1860.2.a.d	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+(-2-\beta )q^{13}-2q^{17}+\cdots$
5580.2.a.h	$5580$	$2$	5580.a	1.a	$1$	$2$	$2$	$44.557$	$\Q(\sqrt{3}) $	None	✓				1860.2.a.e	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}+4q^{11}+(-1-3\beta )q^{13}+\cdots$
5580.2.a.i	$5580$	$2$	5580.a	1.a	$1$	$3$	$3$	$44.557$	3.3.7636.1	None	✓		✓		1860.2.a.h	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-\beta _{1}q^{7}-2q^{11}+\beta _{1}q^{13}+(-1+\cdots)q^{17}+\cdots$
5580.2.a.j	$5580$	$2$	5580.a	1.a	$1$	$3$	$3$	$44.557$	3.3.404.1	None	✓		✓		1860.2.a.g	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{2})q^{7}-2\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots$
5580.2.a.k	$5580$	$2$	5580.a	1.a	$1$	$3$	$3$	$44.557$	3.3.756.1	None	✓				620.2.a.d	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta _{2}q^{7}+(-2-\beta _{2})q^{11}-\beta _{2}q^{13}+\cdots$
5580.2.a.l	$5580$	$2$	5580.a	1.a	$1$	$3$	$3$	$44.557$	3.3.564.1	None	✓				1860.2.a.f	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+2\beta _{1}q^{11}+\cdots$
5580.2.a.m	$5580$	$2$	5580.a	1.a	$1$	$4$	$4$	$44.557$	4.4.224148.1	None	✓				1860.2.a.i	$1$	$0$	$0$	$0$	$-4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{1})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
5580.2.a.n	$5580$	$2$	5580.a	1.a	$1$	$4$	$4$	$44.557$	4.4.25492.1	None	✓				620.2.a.e	$1$	$0$	$0$	$0$	$-4$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(2-\beta _{2}-\beta _{3})q^{7}+(-\beta _{2}-\beta _{3})q^{11}+\cdots$
5580.2.a.o	$5580$	$2$	5580.a	1.a	$1$	$5$	$5$	$44.557$	5.5.10758096.1	None	✓	✓	✓	✓	5580.2.a.o	$1$	$0$	$0$	$0$	$-5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{1})q^{7}+(-\beta _{3}-\beta _{4})q^{11}+\cdots$
5580.2.a.p	$5580$	$2$	5580.a	1.a	$1$	$5$	$5$	$44.557$	5.5.223952.1	None	✓	✓	✓	✓	5580.2.a.p	$1$	$1$	$0$	$0$	$-5$	$4$	$+$	$3$	$\mathrm{SU}(2)$	$q-q^{5}+(1-\beta _{2}+\beta _{3})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
5580.2.a.q	$5580$	$2$	5580.a	1.a	$1$	$5$	$5$	$44.557$	5.5.10758096.1	None	✓	✓	✓	✓	5580.2.a.o	$1$	$1$	$0$	$0$	$5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{1})q^{7}+(\beta _{3}+\beta _{4})q^{11}+\cdots$
5580.2.a.r	$5580$	$2$	5580.a	1.a	$1$	$5$	$5$	$44.557$	5.5.223952.1	None	✓	✓	✓	✓	5580.2.a.p	$1$	$0$	$0$	$0$	$5$	$4$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{5}+(1-\beta _{2}+\beta _{3})q^{7}+(2-\beta _{1}+\beta _{4})q^{11}+\cdots$
5580.2.g.a	$5580$	$2$	5580.g	5.b	$2$	$2$	$2$	$44.557$	$\Q(\sqrt{-1}) $	None					620.2.c.a	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta+1)q^{5}+2\beta q^{7}-4 q^{11}-\beta q^{13}+\cdots$
5580.2.g.b	$5580$	$2$	5580.g	5.b	$2$	$6$	$6$	$44.557$	6.0.84345856.2	None					620.2.c.b	$2$	$0$	$0$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(\beta _{1}-\beta _{5})q^{7}+(-\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots$
5580.2.g.c	$5580$	$2$	5580.g	5.b	$2$	$8$	$8$	$44.557$	8.0.$\cdots$.1	None					620.2.c.c	$2$	$0$	$0$	$0$	$-1$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{5}+(-\beta _{2}-\beta _{7})q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots$
5580.2.g.d	$5580$	$2$	5580.g	5.b	$2$	$14$	$14$	$44.557$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None					1860.2.g.a	$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{9}q^{7}+(-1-\beta _{10})q^{11}+\cdots$
5580.2.g.e	$5580$	$2$	5580.g	5.b	$2$	$14$	$14$	$44.557$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None					1860.2.g.b	$2$	$0$	$0$	$0$	$2$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}-\beta _{12}q^{7}+(-1-\beta _{3})q^{11}+\cdots$
5580.2.g.f	$5580$	$2$	5580.g	5.b	$2$	$16$	$16$	$44.557$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			5580.2.g.f	$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{5}-\beta _{2}q^{7}+\beta _{6}q^{11}+\beta _{12}q^{13}+\cdots$
5580.2.g.g	$5580$	$2$	5580.g	5.b	$2$	$16$	$16$	$44.557$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			5580.2.g.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{5}+\beta _{6}q^{7}+\beta _{9}q^{11}+\beta _{4}q^{13}+\cdots$
5580.2.i.a	$5580$	$2$	5580.i	465.g	$2$	$64$	$64$	$44.557$		None		✓	✓	✓	5580.2.i.a	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5580.2.o.a	$5580$	$2$	5580.o	93.c	$2$	$40$	$40$	$44.557$		None		✓	✓	✓	5580.2.o.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5580.2.br.a	$5580$	$2$	5580.br	93.g	$6$	$88$	$44$	$44.557$		None		✓	✓	✓	5580.2.br.a	$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{6}]$

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Hilbert	Bianchi

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.