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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 (20 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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4256.2.a.a	$4256$	$2$	4256.a	1.a	$1$	$1$	$1$	$33.984$	$\Q$	None	✓	✓			4256.2.a.a	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-3q^{9}-4q^{13}+6q^{17}+\cdots$
4256.2.a.b	$4256$	$2$	4256.a	1.a	$1$	$1$	$1$	$33.984$	$\Q$	None	✓	✓			4256.2.a.a	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}-4q^{13}+6q^{17}+\cdots$
4256.2.a.c	$4256$	$2$	4256.a	1.a	$1$	$2$	$2$	$33.984$	$\Q(\sqrt{5}) $	None	✓	✓			4256.2.a.c	$1$	$0$	$0$	$-3$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+\beta q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots$
4256.2.a.d	$4256$	$2$	4256.a	1.a	$1$	$2$	$2$	$33.984$	$\Q(\sqrt{5}) $	None	✓	✓			4256.2.a.c	$1$	$0$	$0$	$3$	$1$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}-q^{7}+(-1+3\beta )q^{9}+\cdots$
4256.2.a.e	$4256$	$2$	4256.a	1.a	$1$	$4$	$4$	$33.984$	4.4.2624.1	None	✓	✓			4256.2.a.e	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
4256.2.a.f	$4256$	$2$	4256.a	1.a	$1$	$4$	$4$	$33.984$	4.4.2624.1	None	✓	✓			4256.2.a.e	$1$	$1$	$0$	$2$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
4256.2.a.g	$4256$	$2$	4256.a	1.a	$1$	$5$	$5$	$33.984$	5.5.1730752.1	None	✓	✓			4256.2.a.g	$1$	$1$	$0$	$-2$	$-6$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
4256.2.a.h	$4256$	$2$	4256.a	1.a	$1$	$5$	$5$	$33.984$	5.5.1730752.1	None	✓	✓			4256.2.a.g	$1$	$1$	$0$	$2$	$-6$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}-q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
4256.2.a.i	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.41027408.1	None	✓	✓	✓		4256.2.a.i	$1$	$1$	$0$	$-3$	$3$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
4256.2.a.j	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓		4256.2.a.j	$1$	$1$	$0$	$-1$	$-5$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
4256.2.a.k	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.60663248.1	None	✓	✓	✓		4256.2.a.k	$1$	$1$	$0$	$-1$	$1$	$6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{5}q^{5}+q^{7}+(1-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
4256.2.a.l	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			4256.2.a.j	$1$	$0$	$0$	$1$	$-5$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
4256.2.a.m	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.60663248.1	None	✓	✓			4256.2.a.k	$1$	$0$	$0$	$1$	$1$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{5}q^{5}-q^{7}+(1-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
4256.2.a.n	$4256$	$2$	4256.a	1.a	$1$	$6$	$6$	$33.984$	6.6.41027408.1	None	✓	✓			4256.2.a.i	$1$	$0$	$0$	$3$	$3$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
4256.2.a.o	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			4256.2.a.o	$1$	$0$	$0$	$-7$	$5$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1+\beta _{3})q^{5}-q^{7}+\cdots$
4256.2.a.p	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		4256.2.a.p	$1$	$1$	$0$	$-3$	$-5$	$7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
4256.2.a.q	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			4256.2.a.p	$1$	$0$	$0$	$3$	$-5$	$-7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
4256.2.a.r	$4256$	$2$	4256.a	1.a	$1$	$7$	$7$	$33.984$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		4256.2.a.o	$1$	$0$	$0$	$7$	$5$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots$
4256.2.a.s	$4256$	$2$	4256.a	1.a	$1$	$10$	$10$	$33.984$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		4256.2.a.s	$1$	$0$	$0$	$0$	$0$	$-10$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots$
4256.2.a.t	$4256$	$2$	4256.a	1.a	$1$	$10$	$10$	$33.984$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		4256.2.a.s	$1$	$0$	$0$	$0$	$0$	$10$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{5}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots$

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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.