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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 (32 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$ -expansion
1250.2.a.a	$1250$	$2$	1250.a	1.a	$1$	$2$	$2$	$9.981$	$\Q(\sqrt{5})$	None	✓				50.2.d.a	$1$	$1$	$-2$	$-3$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1250.2.a.b	$1250$	$2$	1250.a	1.a	$1$	$2$	$2$	$9.981$	$\Q(\sqrt{5})$	None	✓	✓			1250.2.a.b	$1$	$1$	$-2$	$2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-\beta q^{7}-q^{8}+\cdots$
1250.2.a.c	$1250$	$2$	1250.a	1.a	$1$	$2$	$2$	$9.981$	$\Q(\sqrt{5})$	None	✓	✓			1250.2.a.b	$1$	$1$	$2$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+\beta q^{7}+q^{8}+\cdots$
1250.2.a.d	$1250$	$2$	1250.a	1.a	$1$	$2$	$2$	$9.981$	$\Q(\sqrt{5})$	None	✓				50.2.d.a	$1$	$0$	$2$	$3$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1250.2.a.e	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	$\Q(\zeta_{15})^+$	None	✓	✓			1250.2.a.e	$1$	$0$	$-4$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{6}+\cdots$
1250.2.a.f	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	4.4.7625.1	None	✓		✓		50.2.d.b	$1$	$1$	$-4$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
1250.2.a.g	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	4.4.18625.1	None	✓	✓			1250.2.a.g	$1$	$0$	$-4$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots$
1250.2.a.h	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	$\Q(\zeta_{20})^+$	None	✓				50.2.e.a	$1$	$0$	$-4$	$4$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{6}+\cdots$
1250.2.a.i	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	$\Q(\zeta_{20})^+$	None	✓		✓		50.2.e.a	$1$	$1$	$4$	$-4$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots$
1250.2.a.j	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	4.4.18625.1	None	✓	✓			1250.2.a.g	$1$	$0$	$4$	$1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
1250.2.a.k	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	$\Q(\zeta_{15})^+$	None	✓	✓			1250.2.a.e	$1$	$0$	$4$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
1250.2.a.l	$1250$	$2$	1250.a	1.a	$1$	$4$	$4$	$9.981$	4.4.7625.1	None	✓				50.2.d.b	$1$	$0$	$4$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(1+\beta _{3})q^{7}+\cdots$
1250.2.b.a	$1250$	$2$	1250.b	5.b	$2$	$4$	$4$	$9.981$	$\Q(i, \sqrt{5})$	None		✓			1250.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1250.2.b.b	$1250$	$2$	1250.b	5.b	$2$	$4$	$4$	$9.981$	$\Q(i, \sqrt{5})$	None					50.2.d.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots$
1250.2.b.c	$1250$	$2$	1250.b	5.b	$2$	$8$	$8$	$9.981$	$\Q(\zeta_{20})$	None					50.2.e.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{2}+(-\beta_{2}-\beta_1)q^{3}-q^{4}+\cdots$
1250.2.b.d	$1250$	$2$	1250.b	5.b	$2$	$8$	$8$	$9.981$	8.0. $\cdots$ .2	None		✓			1250.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{6}q^{6}+(2\beta _{4}+\cdots)q^{7}+\cdots$
1250.2.b.e	$1250$	$2$	1250.b	5.b	$2$	$8$	$8$	$9.981$	8.0. $\cdots$ .15	None					50.2.d.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+\beta _{4}-\beta _{7})q^{6}+\cdots$
1250.2.b.f	$1250$	$2$	1250.b	5.b	$2$	$8$	$8$	$9.981$	8.0.324000000.1	None		✓			1250.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-\beta _{3}-\beta _{7})q^{3}-q^{4}-\beta _{2}q^{6}+\cdots$
1250.4.a.a	$1250$	$4$	1250.a	1.a	$1$	$4$	$4$	$73.752$	4.4.33625.1	None	✓	✓			1250.4.a.a	$1$	$1$	$-8$	$-3$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(2\beta _{2}+\beta _{3})q^{3}+4q^{4}+(-4\beta _{2}+\cdots)q^{6}+\cdots$
1250.4.a.b	$1250$	$4$	1250.a	1.a	$1$	$4$	$4$	$73.752$	4.4.33625.1	None	✓	✓			1250.4.a.a	$1$	$1$	$8$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2\beta _{2}-\beta _{3})q^{3}+4q^{4}+(-4\beta _{2}+\cdots)q^{6}+\cdots$
1250.4.a.c	$1250$	$4$	1250.a	1.a	$1$	$6$	$6$	$73.752$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			1250.4.a.c	$1$	$0$	$-12$	$8$	$0$	$-6$	$+$	$5$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
1250.4.a.d	$1250$	$4$	1250.a	1.a	$1$	$6$	$6$	$73.752$	6.6.2140313125.1	None	✓				50.4.d.a	$1$	$0$	$-12$	$8$	$0$	$29$	$+$	$5$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
1250.4.a.e	$1250$	$4$	1250.a	1.a	$1$	$6$	$6$	$73.752$	6.6.2140313125.1	None	✓				50.4.d.a	$1$	$1$	$12$	$-8$	$0$	$-29$	$-$	$5$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots$
1250.4.a.f	$1250$	$4$	1250.a	1.a	$1$	$6$	$6$	$73.752$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			1250.4.a.c	$1$	$0$	$12$	$-8$	$0$	$6$	$+$	$5$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+\cdots$
1250.4.a.g	$1250$	$4$	1250.a	1.a	$1$	$8$	$8$	$73.752$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				50.4.d.b	$1$	$0$	$-16$	$4$	$0$	$27$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
1250.4.a.h	$1250$	$4$	1250.a	1.a	$1$	$8$	$8$	$73.752$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			1250.4.a.h	$1$	$1$	$-16$	$9$	$0$	$22$	$-$	$5^{4}$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-2+2\beta _{1}+\cdots)q^{6}+\cdots$
1250.4.a.i	$1250$	$4$	1250.a	1.a	$1$	$8$	$8$	$73.752$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			1250.4.a.h	$1$	$1$	$16$	$-9$	$0$	$-22$	$-$	$5^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
1250.4.a.j	$1250$	$4$	1250.a	1.a	$1$	$8$	$8$	$73.752$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				50.4.d.b	$1$	$1$	$16$	$-4$	$0$	$-27$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+4q^{4}+\cdots$
1250.4.a.k	$1250$	$4$	1250.a	1.a	$1$	$12$	$12$	$73.752$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		1250.4.a.k	$1$	$0$	$-24$	$-14$	$0$	$-12$	$+$	$5^{9}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{5})q^{3}+4q^{4}+(2-2\beta _{5}+\cdots)q^{6}+\cdots$
1250.4.a.l	$1250$	$4$	1250.a	1.a	$1$	$12$	$12$	$73.752$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			1250.4.a.k	$1$	$0$	$24$	$14$	$0$	$12$	$+$	$5^{9}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{5})q^{3}+4q^{4}+(2-2\beta _{5}+\cdots)q^{6}+\cdots$
1250.4.a.m	$1250$	$4$	1250.a	1.a	$1$	$16$	$16$	$73.752$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		50.4.e.a	$1$	$1$	$-32$	$-12$	$0$	$-56$	$-$	$5^{15}$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{3})q^{3}+4q^{4}+(2-2\beta _{3}+\cdots)q^{6}+\cdots$
1250.4.a.n	$1250$	$4$	1250.a	1.a	$1$	$16$	$16$	$73.752$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓		✓		50.4.e.a	$1$	$0$	$32$	$12$	$0$	$56$	$+$	$5^{15}$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{3})q^{3}+4q^{4}+(2-2\beta _{3}+\cdots)q^{6}+\cdots$

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