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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 (34 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	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9000.2.a.a	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.d	$1$	$1$	$0$	$0$	$0$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{7}+q^{11}+(1+2\beta )q^{13}+\cdots$
9000.2.a.b	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.c	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-2q^{11}+(-2-2\beta )q^{13}+(2+\cdots)q^{17}+\cdots$
9000.2.a.c	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				1000.2.a.b	$1$	$0$	$0$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-2\beta )q^{7}+(3+2\beta )q^{11}+(4-\beta )q^{13}+\cdots$
9000.2.a.d	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓	✓			9000.2.a.d	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{7}+(-2+2\beta )q^{11}+2\beta q^{13}+\cdots$
9000.2.a.e	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓	✓			9000.2.a.d	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{7}+(2-2\beta )q^{11}+2\beta q^{13}+(1+\cdots)q^{17}+\cdots$
9000.2.a.f	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				1000.2.a.a	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{7}+(-2+2\beta )q^{11}+(-2+2\beta )q^{13}+\cdots$
9000.2.a.g	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.a	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{7}+3q^{11}+3q^{13}-3\beta q^{17}+\cdots$
9000.2.a.h	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{11}+(-4+2\beta )q^{13}+(6-3\beta )q^{17}+\cdots$
9000.2.a.i	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{11}+(4-2\beta )q^{13}+(-6+3\beta )q^{17}+\cdots$
9000.2.a.j	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				1000.2.a.a	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{7}+(-2+2\beta )q^{11}+(2-2\beta )q^{13}+\cdots$
9000.2.a.k	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.a	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{7}+3q^{11}-3q^{13}+3\beta q^{17}+\cdots$
9000.2.a.l	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓	✓			9000.2.a.d	$1$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{7}+(-2+2\beta )q^{11}-2\beta q^{13}+\cdots$
9000.2.a.m	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓	✓			9000.2.a.d	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{7}+(2-2\beta )q^{11}-2\beta q^{13}+(-1+\cdots)q^{17}+\cdots$
9000.2.a.n	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.c	$1$	$1$	$0$	$0$	$0$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-2q^{11}+(2+2\beta )q^{13}+(-2+\cdots)q^{17}+\cdots$
9000.2.a.o	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				1000.2.a.b	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+2\beta )q^{7}+(3+2\beta )q^{11}+(-4+\beta )q^{13}+\cdots$
9000.2.a.p	$9000$	$2$	9000.a	1.a	$1$	$2$	$2$	$71.865$	$\Q(\sqrt{5}) $	None	✓				3000.2.a.d	$1$	$0$	$0$	$0$	$0$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{7}+q^{11}+(-3+2\beta )q^{13}+\cdots$
9000.2.a.q	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.10025.1	None	✓				1000.2.a.f	$1$	$1$	$0$	$0$	$0$	$-9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta _{2}+\beta _{3})q^{7}+(-1-\beta _{1})q^{11}+\cdots$
9000.2.a.r	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.4400.1	None	✓				1000.2.a.e	$1$	$0$	$0$	$0$	$0$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2}+\beta _{3})q^{7}+2\beta _{3}q^{11}+(2\beta _{1}+\cdots)q^{13}+\cdots$
9000.2.a.s	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.13025.1	None	✓				3000.2.a.i	$1$	$0$	$0$	$0$	$0$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{7}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{11}+\cdots$
9000.2.a.t	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.47025.1	None	✓				3000.2.a.j	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}+\beta _{2})q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots$
9000.2.a.u	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.13025.1	None	✓				3000.2.a.k	$1$	$1$	$0$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{3})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
9000.2.a.v	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.36025.1	None	✓				3000.2.a.l	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{7}+(1+2\beta _{2}+\beta _{3})q^{11}+(1+2\beta _{2}+\cdots)q^{13}+\cdots$
9000.2.a.w	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.36025.1	None	✓				3000.2.a.l	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{7}+(1+2\beta _{2}+\beta _{3})q^{11}+(-1+\cdots)q^{13}+\cdots$
9000.2.a.x	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.13025.1	None	✓				3000.2.a.k	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
9000.2.a.y	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.47025.1	None	✓				3000.2.a.j	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}-\beta _{2})q^{7}+(\beta _{1}-2\beta _{2})q^{11}+\cdots$
9000.2.a.z	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.13025.1	None	✓				3000.2.a.i	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{7}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{11}+\cdots$
9000.2.a.ba	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.4400.1	None	✓				1000.2.a.e	$1$	$1$	$0$	$0$	$0$	$6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta _{2}+\beta _{3})q^{7}-2\beta _{3}q^{11}+(2\beta _{1}+\cdots)q^{13}+\cdots$
9000.2.a.bb	$9000$	$2$	9000.a	1.a	$1$	$4$	$4$	$71.865$	4.4.10025.1	None	✓				1000.2.a.f	$1$	$1$	$0$	$0$	$0$	$9$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta _{3})q^{7}+(-2+\beta _{1}-\beta _{2})q^{11}+\cdots$
9000.2.a.bc	$9000$	$2$	9000.a	1.a	$1$	$6$	$6$	$71.865$	6.6.239482000.1	None	✓	✓	✓		9000.2.a.bc	$1$	$1$	$0$	$0$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{7}+(\beta _{3}-\beta _{5})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots$
9000.2.a.bd	$9000$	$2$	9000.a	1.a	$1$	$6$	$6$	$71.865$	6.6.239482000.1	None	✓	✓	✓		9000.2.a.bc	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{7}+(-\beta _{3}+\beta _{5})q^{11}+\cdots$
9000.2.a.be	$9000$	$2$	9000.a	1.a	$1$	$6$	$6$	$71.865$	6.6.239482000.1	None	✓	✓			9000.2.a.bc	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{7}+(\beta _{3}-\beta _{5})q^{11}+(\beta _{2}+\beta _{5})q^{13}+\cdots$
9000.2.a.bf	$9000$	$2$	9000.a	1.a	$1$	$6$	$6$	$71.865$	6.6.239482000.1	None	✓	✓			9000.2.a.bc	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{7}+(-\beta _{3}+\beta _{5})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots$
9000.2.a.bg	$9000$	$2$	9000.a	1.a	$1$	$8$	$8$	$71.865$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		9000.2.a.bg	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{7}+(-\beta _{2}+\beta _{7})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots$
9000.2.a.bh	$9000$	$2$	9000.a	1.a	$1$	$8$	$8$	$71.865$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		9000.2.a.bg	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{7}+(\beta _{2}-\beta _{7})q^{11}+(-\beta _{2}-\beta _{4}+\cdots)q^{13}+\cdots$

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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.