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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (21 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4680.2.a.a	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-5$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-5q^{7}-q^{11}+q^{13}+3q^{17}+\cdots$
4680.2.a.b	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots$
4680.2.a.c	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+3q^{11}-q^{13}+q^{17}+\cdots$
4680.2.a.e	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}+q^{13}-2q^{17}+2q^{19}+\cdots$
4680.2.a.f	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{13}+6q^{17}-8q^{19}-6q^{23}+\cdots$
4680.2.a.g	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{11}+q^{13}-2q^{17}-4q^{19}+\cdots$
4680.2.a.i	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-4q^{11}-q^{13}+2q^{19}+\cdots$
4680.2.a.j	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}+5q^{11}-q^{13}-3q^{17}+\cdots$
4680.2.a.k	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-4q^{11}+q^{13}-6q^{17}+\cdots$
4680.2.a.m	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-4q^{11}+q^{13}+6q^{17}+\cdots$
4680.2.a.n	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots$
4680.2.a.o	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+5q^{11}+q^{13}-3q^{17}+\cdots$
4680.2.a.p	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{11}+q^{13}+2q^{17}-4q^{19}+\cdots$
4680.2.a.r	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{13}-6q^{17}-8q^{19}+6q^{23}+\cdots$
4680.2.a.v	$4680$	$2$	4680.a	1.a	$1$	$1$	$1$	$37.370$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+3q^{7}-5q^{11}-q^{13}+3q^{17}+\cdots$
4680.2.a.x	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$-4$	$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-q^{13}+(2-\beta )q^{17}+2q^{19}+\cdots$
4680.2.a.z	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
4680.2.a.ba	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-4$	$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-q^{13}+(-2-\beta )q^{17}+\cdots$
4680.2.a.bb	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}+(2+\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
4680.2.a.bc	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(-3-\beta )q^{11}-q^{13}-2q^{17}+\cdots$
4680.2.a.bd	$4680$	$2$	4680.a	1.a	$1$	$2$	$2$	$37.370$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2\beta q^{7}+(-1-\beta )q^{11}+q^{13}+\cdots$

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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.