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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 (43 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	13	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7774.2.a.a	$7774$	$2$	7774.a	1.a	$1$	$1$	$1$	$62.076$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-3$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots$
7774.2.a.b	$7774$	$2$	7774.a	1.a	$1$	$1$	$1$	$62.076$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
7774.2.a.c	$7774$	$2$	7774.a	1.a	$1$	$1$	$1$	$62.076$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}+3q^{5}-3q^{6}-3q^{7}+\cdots$
7774.2.a.d	$7774$	$2$	7774.a	1.a	$1$	$1$	$1$	$62.076$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots$
7774.2.a.e	$7774$	$2$	7774.a	1.a	$1$	$1$	$1$	$62.076$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}+2q^{11}+q^{16}+\cdots$
7774.2.a.f	$7774$	$2$	7774.a	1.a	$1$	$2$	$2$	$62.076$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$-2$	$2$	$6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1+2\beta )q^{5}+\cdots$
7774.2.a.g	$7774$	$2$	7774.a	1.a	$1$	$2$	$2$	$62.076$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$4$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots$
7774.2.a.h	$7774$	$2$	7774.a	1.a	$1$	$2$	$2$	$62.076$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$-2$	$4$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-\beta q^{5}-2q^{6}+\beta q^{7}+\cdots$
7774.2.a.i	$7774$	$2$	7774.a	1.a	$1$	$2$	$2$	$62.076$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$-2$	$-4$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-2+\beta )q^{5}+\cdots$
7774.2.a.j	$7774$	$2$	7774.a	1.a	$1$	$2$	$2$	$62.076$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$0$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
7774.2.a.k	$7774$	$2$	7774.a	1.a	$1$	$2$	$2$	$62.076$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$1$	$-1$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+(2+\cdots)q^{7}+\cdots$
7774.2.a.l	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	3.3.1076.1	None	✓	$1$	$0$	$-3$	$-3$	$-3$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots$
7774.2.a.m	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$-3$	$5$	$5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots$
7774.2.a.n	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$2$	$-1$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots$
7774.2.a.o	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	3.3.148.1	None	✓	$1$	$0$	$-3$	$2$	$6$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(2-\beta _{2})q^{5}+\cdots$
7774.2.a.p	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$-3$	$-5$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
7774.2.a.q	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	3.3.1076.1	None	✓	$1$	$1$	$3$	$-3$	$3$	$-7$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
7774.2.a.r	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	3.3.148.1	None	✓	$1$	$1$	$3$	$2$	$-6$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots$
7774.2.a.s	$7774$	$2$	7774.a	1.a	$1$	$3$	$3$	$62.076$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$3$	$2$	$1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots$
7774.2.a.t	$7774$	$2$	7774.a	1.a	$1$	$4$	$4$	$62.076$	$\Q(\sqrt{3}, \sqrt{11})$	None	✓	$1$	$0$	$4$	$0$	$4$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
7774.2.a.u	$7774$	$2$	7774.a	1.a	$1$	$5$	$5$	$62.076$	5.5.674848.1	None	✓	$1$	$0$	$-5$	$2$	$2$	$-2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
7774.2.a.v	$7774$	$2$	7774.a	1.a	$1$	$6$	$6$	$62.076$	6.6.9925933.1	None	✓	$1$	$0$	$-6$	$-2$	$3$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{5}q^{3}+q^{4}+(1+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
7774.2.a.w	$7774$	$2$	7774.a	1.a	$1$	$6$	$6$	$62.076$	6.6.127049661.1	None	✓	$1$	$1$	$-6$	$2$	$-7$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{4}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots$
7774.2.a.x	$7774$	$2$	7774.a	1.a	$1$	$6$	$6$	$62.076$	6.6.152089744.1	None	✓	$1$	$1$	$-6$	$3$	$-7$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
7774.2.a.y	$7774$	$2$	7774.a	1.a	$1$	$6$	$6$	$62.076$	6.6.9925933.1	None	✓	$1$	$1$	$6$	$-2$	$-3$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{5}q^{3}+q^{4}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
7774.2.a.z	$7774$	$2$	7774.a	1.a	$1$	$6$	$6$	$62.076$	6.6.127049661.1	None	✓	$1$	$0$	$6$	$2$	$7$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{4}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{4}q^{6}+\cdots$
7774.2.a.ba	$7774$	$2$	7774.a	1.a	$1$	$6$	$6$	$62.076$	6.6.152089744.1	None	✓	$1$	$0$	$6$	$3$	$7$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots$
7774.2.a.bb	$7774$	$2$	7774.a	1.a	$1$	$7$	$7$	$62.076$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$-2$	$4$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{3})q^{5}+\beta _{1}q^{6}+\cdots$
7774.2.a.bc	$7774$	$2$	7774.a	1.a	$1$	$7$	$7$	$62.076$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$2$	$-6$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots$
7774.2.a.bd	$7774$	$2$	7774.a	1.a	$1$	$7$	$7$	$62.076$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$7$	$-2$	$-4$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots$
7774.2.a.be	$7774$	$2$	7774.a	1.a	$1$	$7$	$7$	$62.076$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$7$	$2$	$6$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{3}q^{6}+\cdots$
7774.2.a.bf	$7774$	$2$	7774.a	1.a	$1$	$9$	$9$	$62.076$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
7774.2.a.bg	$7774$	$2$	7774.a	1.a	$1$	$9$	$9$	$62.076$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$-3$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
7774.2.a.bh	$7774$	$2$	7774.a	1.a	$1$	$12$	$12$	$62.076$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-12$	$-9$	$4$	$7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(\beta _{2}-\beta _{10}+\cdots)q^{5}+\cdots$
7774.2.a.bi	$7774$	$2$	7774.a	1.a	$1$	$12$	$12$	$62.076$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-12$	$-2$	$8$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{10})q^{5}+\cdots$
7774.2.a.bj	$7774$	$2$	7774.a	1.a	$1$	$12$	$12$	$62.076$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$12$	$-9$	$-4$	$-7$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
7774.2.a.bk	$7774$	$2$	7774.a	1.a	$1$	$12$	$12$	$62.076$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$12$	$-2$	$-8$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{10})q^{5}+\cdots$
7774.2.a.bl	$7774$	$2$	7774.a	1.a	$1$	$14$	$14$	$62.076$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-14$	$4$	$-8$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{9})q^{5}+\cdots$
7774.2.a.bm	$7774$	$2$	7774.a	1.a	$1$	$14$	$14$	$62.076$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$14$	$4$	$8$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{9})q^{5}+\beta _{1}q^{6}+\cdots$
7774.2.a.bn	$7774$	$2$	7774.a	1.a	$1$	$18$	$18$	$62.076$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$-18$	$3$	$-2$	$-15$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{11}q^{5}-\beta _{1}q^{6}+\cdots$
7774.2.a.bo	$7774$	$2$	7774.a	1.a	$1$	$18$	$18$	$62.076$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$18$	$3$	$2$	$15$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{11}q^{5}+\beta _{1}q^{6}+\cdots$
7774.2.a.bp	$7774$	$2$	7774.a	1.a	$1$	$21$	$21$	$62.076$		None	✓	$1$	$0$	$-21$	$8$	$-2$	$-13$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
7774.2.a.bq	$7774$	$2$	7774.a	1.a	$1$	$21$	$21$	$62.076$		None	✓	$1$	$0$	$21$	$8$	$2$	$13$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.