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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 (44 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
4620.2.a.a	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
4620.2.a.b	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
4620.2.a.c	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
4620.2.a.d	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
4620.2.a.e	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
4620.2.a.f	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
4620.2.a.g	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
4620.2.a.h	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{15}+\cdots$
4620.2.a.i	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{15}+\cdots$
4620.2.a.j	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
4620.2.a.k	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
4620.2.a.l	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-6q^{13}+\cdots$
4620.2.a.m	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+q^{15}+\cdots$
4620.2.a.n	$4620$	$2$	4620.a	1.a	$1$	$1$	$1$	$36.891$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
4620.2.a.o	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	$\Q(\sqrt{7}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}+(-3+\cdots)q^{13}+\cdots$
4620.2.a.p	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
4620.2.a.q	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	$\Q(\sqrt{73}) $	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
4620.2.a.r	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}+q^{11}+(2+\beta )q^{13}+\cdots$
4620.2.a.s	$4620$	$2$	4620.a	1.a	$1$	$2$	$2$	$36.891$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+(-5+\cdots)q^{13}+\cdots$
4620.2.a.t	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.1944.1	None	✓	$1$	$0$	$0$	$-3$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-\beta _{2}q^{13}+\cdots$
4620.2.a.u	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.8220.1	None	✓	$1$	$0$	$0$	$3$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots$
4620.2.a.v	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.1016.1	None	✓	$1$	$0$	$0$	$3$	$-3$	$3$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots$
4620.2.a.w	$4620$	$2$	4620.a	1.a	$1$	$3$	$3$	$36.891$	3.3.3576.1	None	✓	$1$	$0$	$0$	$3$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots$
4620.2.a.x	$4620$	$2$	4620.a	1.a	$1$	$4$	$4$	$36.891$	4.4.138892.1	None	✓	$1$	$0$	$0$	$4$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+(1+\beta _{3})q^{13}+\cdots$
4620.2.f.a	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$1$	$0$	$-4$	$-3$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$
4620.2.f.b	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$0$	$-4$	$-3$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(2+\beta _{2}+\cdots)q^{7}+\cdots$
4620.2.f.c	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$0$	$4$	$3$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$
4620.2.f.d	$4620$	$2$	4620.f	385.h	$2$	$4$	$4$	$36.891$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$0$	$4$	$3$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(2+\beta _{2})q^{7}+\cdots$
4620.2.f.e	$4620$	$2$	4620.f	385.h	$2$	$40$	$40$	$36.891$		None		$4$	$0$	$0$	$-40$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
4620.2.f.f	$4620$	$2$	4620.f	385.h	$2$	$40$	$40$	$36.891$		None		$4$	$0$	$0$	$40$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
4620.2.h.a	$4620$	$2$	4620.h	5.b	$2$	$2$	$2$	$36.891$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1-2i)q^{5}-iq^{7}-q^{9}-q^{11}+\cdots$
4620.2.h.b	$4620$	$2$	4620.h	5.b	$2$	$2$	$2$	$36.891$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(2-i)q^{5}-iq^{7}-q^{9}-q^{11}+\cdots$
4620.2.h.c	$4620$	$2$	4620.h	5.b	$2$	$2$	$2$	$36.891$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(2+i)q^{5}+iq^{7}-q^{9}+q^{11}+\cdots$
4620.2.h.d	$4620$	$2$	4620.h	5.b	$2$	$14$	$14$	$36.891$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{4}q^{5}+\beta _{3}q^{7}-q^{9}-q^{11}+\cdots$
4620.2.h.e	$4620$	$2$	4620.h	5.b	$2$	$14$	$14$	$36.891$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{2}q^{7}-q^{9}+q^{11}+\cdots$
4620.2.h.f	$4620$	$2$	4620.h	5.b	$2$	$14$	$14$	$36.891$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+\beta _{7}q^{5}+\beta _{6}q^{7}-q^{9}-q^{11}+\cdots$
4620.2.h.g	$4620$	$2$	4620.h	5.b	$2$	$16$	$16$	$36.891$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{3}+\beta _{4}q^{5}+\beta _{8}q^{7}-q^{9}+q^{11}+\cdots$
4620.2.m.a	$4620$	$2$	4620.m	33.d	$2$	$48$	$48$	$36.891$		None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4620.2.m.b	$4620$	$2$	4620.m	33.d	$2$	$48$	$48$	$36.891$		None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
4620.2.be.a	$4620$	$2$	4620.be	77.b	$2$	$4$	$4$	$36.891$	$\Q(i, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}-q^{9}+(2+\cdots)q^{11}+\cdots$
4620.2.be.b	$4620$	$2$	4620.be	77.b	$2$	$4$	$4$	$36.891$	$\Q(i, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}-q^{9}+(2+\cdots)q^{11}+\cdots$
4620.2.be.c	$4620$	$2$	4620.be	77.b	$2$	$12$	$12$	$36.891$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}+\beta _{7}q^{5}+\beta _{8}q^{7}-q^{9}+(-1+\cdots)q^{11}+\cdots$
4620.2.be.d	$4620$	$2$	4620.be	77.b	$2$	$12$	$12$	$36.891$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{3}+\beta _{10}q^{5}+(-\beta _{3}+\beta _{4})q^{7}+\cdots$
4620.2.be.e	$4620$	$2$	4620.be	77.b	$2$	$32$	$32$	$36.891$		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 $\Q$
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.