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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (31 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6664.2.a.a	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	$\Q$	None	✓				952.2.q.b	$1$	$0$	$0$	$-3$	$2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}+6q^{9}+5q^{11}-7q^{13}+\cdots$
6664.2.a.b	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	$\Q$	None	✓				136.2.a.b	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+2q^{11}+6q^{13}+q^{17}+\cdots$
6664.2.a.c	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	$\Q$	None	✓				952.2.q.a	$1$	$1$	$0$	$0$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{11}-4q^{13}+q^{17}+\cdots$
6664.2.a.d	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	$\Q$	None	✓				952.2.q.a	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+2q^{11}+4q^{13}-q^{17}+\cdots$
6664.2.a.e	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	$\Q$	None	✓				136.2.a.a	$1$	$1$	$0$	$2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{9}-6q^{11}-2q^{13}+\cdots$
6664.2.a.f	$6664$	$2$	6664.a	1.a	$1$	$1$	$1$	$53.212$	$\Q$	None	✓				952.2.q.b	$1$	$0$	$0$	$3$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}+6q^{9}+5q^{11}+7q^{13}+\cdots$
6664.2.a.g	$6664$	$2$	6664.a	1.a	$1$	$2$	$2$	$53.212$	$\Q(\sqrt{13}) $	None	✓				952.2.a.b	$1$	$1$	$0$	$-1$	$3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{5}+\beta q^{9}+(2-2\beta )q^{11}+\cdots$
6664.2.a.h	$6664$	$2$	6664.a	1.a	$1$	$2$	$2$	$53.212$	$\Q(\sqrt{5}) $	None	✓				952.2.a.a	$1$	$0$	$0$	$1$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
6664.2.a.i	$6664$	$2$	6664.a	1.a	$1$	$2$	$2$	$53.212$	$\Q(\sqrt{5}) $	None	✓				136.2.a.c	$1$	$0$	$0$	$2$	$-4$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2q^{5}+(3+2\beta )q^{9}+(1+\cdots)q^{11}+\cdots$
6664.2.a.j	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.229.1	None	✓				952.2.a.f	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}-2\beta _{2})q^{9}+\cdots$
6664.2.a.k	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.1229.1	None	✓				952.2.a.e	$1$	$0$	$0$	$1$	$-3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots$
6664.2.a.l	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.229.1	None	✓				952.2.a.d	$1$	$1$	$0$	$3$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+(1-2\beta _{1}+\beta _{2})q^{9}+\cdots$
6664.2.a.m	$6664$	$2$	6664.a	1.a	$1$	$3$	$3$	$53.212$	3.3.229.1	None	✓				952.2.a.c	$1$	$0$	$0$	$3$	$5$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(2+\beta _{2})q^{5}+(1+2\beta _{1}+\cdots)q^{9}+\cdots$
6664.2.a.n	$6664$	$2$	6664.a	1.a	$1$	$4$	$4$	$53.212$	$\Q(\sqrt{14 +2 \sqrt{41}})$	None	✓				952.2.a.h	$1$	$1$	$0$	$-3$	$-5$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(2+\cdots)q^{9}+\cdots$
6664.2.a.o	$6664$	$2$	6664.a	1.a	$1$	$4$	$4$	$53.212$	$\Q(\sqrt{62 +10 \sqrt{5}})$	None	✓				952.2.a.g	$1$	$0$	$0$	$-3$	$1$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
6664.2.a.p	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.13431004.1	None	✓	✓			6664.2.a.p	$1$	$1$	$0$	$-4$	$-2$	$0$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}-\beta _{3}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
6664.2.a.q	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.15751800.1	None	✓	✓			6664.2.a.q	$1$	$0$	$0$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
6664.2.a.r	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.30091192.1	None	✓				952.2.q.c	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{2}q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6664.2.a.s	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.30091192.1	None	✓				952.2.q.c	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6664.2.a.t	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.15751800.1	None	✓	✓			6664.2.a.q	$1$	$1$	$0$	$2$	$-4$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
6664.2.a.u	$6664$	$2$	6664.a	1.a	$1$	$6$	$6$	$53.212$	6.6.13431004.1	None	✓	✓			6664.2.a.p	$1$	$0$	$0$	$4$	$2$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+\beta _{3}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots$
6664.2.a.v	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				952.2.q.e	$1$	$1$	$0$	$-3$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{5}+(\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
6664.2.a.w	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				952.2.q.d	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{2}q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots$
6664.2.a.x	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		952.2.q.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{2}q^{9}+(\beta _{3}+\beta _{6})q^{11}+\cdots$
6664.2.a.y	$6664$	$2$	6664.a	1.a	$1$	$7$	$7$	$53.212$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		952.2.q.e	$1$	$1$	$0$	$3$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}+(\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
6664.2.a.z	$6664$	$2$	6664.a	1.a	$1$	$10$	$10$	$53.212$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		952.2.q.f	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{7}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6664.2.a.ba	$6664$	$2$	6664.a	1.a	$1$	$10$	$10$	$53.212$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				952.2.q.f	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
6664.2.a.bb	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		6664.2.a.bb	$1$	$1$	$0$	$-8$	$-4$	$0$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+\beta _{3}q^{5}+(1-\beta _{1}+\beta _{6}+\cdots)q^{9}+\cdots$
6664.2.a.bc	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		6664.2.a.bc	$1$	$0$	$0$	$-4$	$8$	$0$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{10})q^{5}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
6664.2.a.bd	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		6664.2.a.bc	$1$	$1$	$0$	$4$	$-8$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{10})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6664.2.a.be	$6664$	$2$	6664.a	1.a	$1$	$12$	$12$	$53.212$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		6664.2.a.bb	$1$	$0$	$0$	$8$	$4$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{3}q^{5}+(1-\beta _{1}+\beta _{6}+\cdots)q^{9}+\cdots$

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Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
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.