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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 (32 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4536.2.a.a	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}-3q^{11}+4q^{13}-6q^{17}+\cdots$
4536.2.a.b	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{11}+2q^{17}-2q^{19}+\cdots$
4536.2.a.c	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+3q^{11}-6q^{13}-7q^{17}+\cdots$
4536.2.a.d	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-6q^{11}+6q^{13}-2q^{17}+\cdots$
4536.2.a.e	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+3q^{13}+7q^{17}+4q^{19}+\cdots$
4536.2.a.f	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+3q^{13}-7q^{17}+4q^{19}+\cdots$
4536.2.a.g	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+6q^{11}+6q^{13}+2q^{17}+\cdots$
4536.2.a.h	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{11}-6q^{13}+7q^{17}+\cdots$
4536.2.a.i	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+3q^{11}-2q^{17}-2q^{19}+\cdots$
4536.2.a.j	$4536$	$2$	4536.a	1.a	$1$	$1$	$1$	$36.220$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}+3q^{11}+4q^{13}+6q^{17}+\cdots$
4536.2.a.k	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}-q^{7}+(-3-\beta )q^{11}+\cdots$
4536.2.a.l	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$0$	$-4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+(-2-\beta )q^{11}-4q^{13}+\cdots$
4536.2.a.m	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+(-1+\beta )q^{11}-q^{13}+\cdots$
4536.2.a.n	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}-q^{7}+(-1+\beta )q^{11}+(4-\beta )q^{13}+\cdots$
4536.2.a.o	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(1-\beta )q^{11}+(4-\beta )q^{13}+\cdots$
4536.2.a.p	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+(1+\beta )q^{11}-q^{13}-\beta q^{17}+\cdots$
4536.2.a.q	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+(2-\beta )q^{11}-4q^{13}+\cdots$
4536.2.a.r	$4536$	$2$	4536.a	1.a	$1$	$2$	$2$	$36.220$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}-q^{7}+(3-\beta )q^{11}+(1-2\beta )q^{13}+\cdots$
4536.2.a.s	$4536$	$2$	4536.a	1.a	$1$	$3$	$3$	$36.220$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}+q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots$
4536.2.a.t	$4536$	$2$	4536.a	1.a	$1$	$3$	$3$	$36.220$	3.3.837.1	None	✓	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+q^{7}+(-1+\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots$
4536.2.a.u	$4536$	$2$	4536.a	1.a	$1$	$3$	$3$	$36.220$	3.3.837.1	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+q^{7}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots$
4536.2.a.v	$4536$	$2$	4536.a	1.a	$1$	$3$	$3$	$36.220$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots$
4536.2.a.w	$4536$	$2$	4536.a	1.a	$1$	$4$	$4$	$36.220$	4.4.25488.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}+\beta _{2})q^{5}+q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
4536.2.a.x	$4536$	$2$	4536.a	1.a	$1$	$4$	$4$	$36.220$	4.4.22545.1	None	✓	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{3})q^{5}+q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots$
4536.2.a.y	$4536$	$2$	4536.a	1.a	$1$	$4$	$4$	$36.220$	4.4.45729.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-q^{7}+(2-\beta _{1})q^{11}+\cdots$
4536.2.a.z	$4536$	$2$	4536.a	1.a	$1$	$4$	$4$	$36.220$	4.4.45729.1	None	✓	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}-q^{7}+(-2+\beta _{1})q^{11}+\cdots$
4536.2.a.ba	$4536$	$2$	4536.a	1.a	$1$	$4$	$4$	$36.220$	4.4.22545.1	None	✓	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{3})q^{5}+q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
4536.2.a.bb	$4536$	$2$	4536.a	1.a	$1$	$4$	$4$	$36.220$	4.4.25488.1	None	✓	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{2})q^{5}+q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
4536.2.a.bc	$4536$	$2$	4536.a	1.a	$1$	$5$	$5$	$36.220$	5.5.1425384.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$-5$	$-$	$3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}-q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
4536.2.a.bd	$4536$	$2$	4536.a	1.a	$1$	$5$	$5$	$36.220$	5.5.1425384.1	None	✓	$1$	$0$	$0$	$0$	$3$	$-5$	$-$	$3$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}-q^{7}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
4536.2.k.a	$4536$	$2$	4536.k	21.c	$2$	$48$	$48$	$36.220$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4536.2.k.b	$4536$	$2$	4536.k	21.c	$2$	$48$	$48$	$36.220$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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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.