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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 (48 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2760.1.o.a	$2760$	$1$	2760.o	2760.o	$2$	$1$	$1$	$1.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-690}) $	$\Q(\sqrt{46}) $	✓	$4$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
2760.1.o.b	$2760$	$1$	2760.o	2760.o	$2$	$1$	$1$	$1.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-690}) $	$\Q(\sqrt{46}) $	✓	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
2760.1.o.c	$2760$	$1$	2760.o	2760.o	$2$	$1$	$1$	$1.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-690}) $	$\Q(\sqrt{46}) $	✓	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
2760.1.o.d	$2760$	$1$	2760.o	2760.o	$2$	$1$	$1$	$1.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-690}) $	$\Q(\sqrt{46}) $	✓	$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
2760.1.bv.a	$2760$	$1$	2760.bv	345.l	$4$	$4$	$2$	$1.377$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots$
2760.1.bv.b	$2760$	$1$	2760.bv	345.l	$4$	$4$	$2$	$1.377$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+q^{3}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots$
2760.1.cm.a	$2760$	$1$	2760.cm	2760.bm	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$0$		$1$		$q+\zeta_{22}^{8}q^{2}-\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots$
2760.1.cm.b	$2760$	$1$	2760.cm	2760.bm	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q+\zeta_{22}^{8}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots$
2760.1.cm.c	$2760$	$1$	2760.cm	2760.bm	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots$
2760.1.cm.d	$2760$	$1$	2760.cm	2760.bm	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$1$	$1$	$-1$	$0$		$1$		$q-\zeta_{22}^{8}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}^{5}q^{4}+\cdots$
2760.1.cm.e	$2760$	$1$	2760.cm	2760.bm	$22$	$20$	$2$	$1.377$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{44}^{3}q^{2}+\zeta_{44}^{21}q^{3}+\zeta_{44}^{6}q^{4}+\cdots$
2760.1.cm.f	$2760$	$1$	2760.cm	2760.bm	$22$	$20$	$2$	$1.377$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{44}^{5}q^{2}-\zeta_{44}^{21}q^{3}+\zeta_{44}^{10}q^{4}+\cdots$
2760.1.co.a	$2760$	$1$	2760.co	2760.bo	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-\zeta_{22}^{5}q^{2}-\zeta_{22}^{2}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
2760.1.co.b	$2760$	$1$	2760.co	2760.bo	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-\zeta_{22}q^{2}-\zeta_{22}^{2}q^{3}+\zeta_{22}^{2}q^{4}+\zeta_{22}^{7}q^{5}+\cdots$
2760.1.co.c	$2760$	$1$	2760.co	2760.bo	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+\zeta_{22}q^{2}+\zeta_{22}^{2}q^{3}+\zeta_{22}^{2}q^{4}-\zeta_{22}^{7}q^{5}+\cdots$
2760.1.co.d	$2760$	$1$	2760.co	2760.bo	$22$	$10$	$1$	$1.377$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{2}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
2760.2.a.a	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
2760.2.a.b	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
2760.2.a.c	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
2760.2.a.d	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
2760.2.a.e	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
2760.2.a.f	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{13}-q^{15}+\cdots$
2760.2.a.g	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
2760.2.a.h	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots$
2760.2.a.i	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
2760.2.a.j	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-4q^{11}+q^{15}+\cdots$
2760.2.a.k	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+2q^{11}+q^{15}+6q^{17}+\cdots$
2760.2.a.l	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	$\Q(\sqrt{11}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots$
2760.2.a.m	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots$
2760.2.a.n	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1+2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
2760.2.a.o	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}+q^{9}+4q^{11}+(-2+\cdots)q^{13}+\cdots$
2760.2.a.p	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-\beta q^{7}+q^{9}-2\beta q^{11}+\cdots$
2760.2.a.q	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots$
2760.2.a.r	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(-2+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
2760.2.a.s	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.1436.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
2760.2.a.t	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(1-\beta _{2})q^{13}+\cdots$
2760.2.a.u	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.568.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(1-2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
2760.2.a.v	$2760$	$2$	2760.a	1.a	$1$	$4$	$4$	$22.039$	4.4.54764.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-4$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{3}q^{11}+\cdots$
2760.2.a.w	$2760$	$2$	2760.a	1.a	$1$	$5$	$5$	$22.039$	5.5.20087896.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-5$	$5$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
2760.2.k.a	$2760$	$2$	2760.k	5.b	$2$	$2$	$2$	$22.039$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots$
2760.2.k.b	$2760$	$2$	2760.k	5.b	$2$	$2$	$2$	$22.039$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(-1+2i)q^{5}-q^{9}+(2+i)q^{15}+\cdots$
2760.2.k.c	$2760$	$2$	2760.k	5.b	$2$	$12$	$12$	$22.039$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}-\beta _{10}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots$
2760.2.k.d	$2760$	$2$	2760.k	5.b	$2$	$14$	$14$	$22.039$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{12}q^{5}+(\beta _{2}+\beta _{10})q^{7}+\cdots$
2760.2.k.e	$2760$	$2$	2760.k	5.b	$2$	$16$	$16$	$22.039$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{1}q^{7}-q^{9}+\beta _{14}q^{11}+\cdots$
2760.2.k.f	$2760$	$2$	2760.k	5.b	$2$	$22$	$22$	$22.039$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
2760.2.p.a	$2760$	$2$	2760.p	69.c	$2$	$48$	$48$	$22.039$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-48$	$0$			$\mathrm{SU}(2)[C_{2}]$
2760.2.p.b	$2760$	$2$	2760.p	69.c	$2$	$48$	$48$	$22.039$		$_{}$	None	None		$2$	$0$	$0$	$0$	$48$	$0$			$\mathrm{SU}(2)[C_{2}]$
2760.3.g.a	$2760$	$3$	2760.g	23.b	$2$	$96$	$96$	$75.205$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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