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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 (29 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	11	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5225.2.a.a	$5225$	$2$	5225.a	1.a	$1$	$1$	$1$	$41.722$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{11}-2q^{13}+\cdots$
5225.2.a.b	$5225$	$2$	5225.a	1.a	$1$	$1$	$1$	$41.722$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+4q^{7}-2q^{9}+q^{11}+\cdots$
5225.2.a.c	$5225$	$2$	5225.a	1.a	$1$	$1$	$1$	$41.722$	$\Q$	None	✓	$1$	$1$	$1$	$2$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}-q^{4}+2q^{6}+2q^{7}-3q^{8}+\cdots$
5225.2.a.d	$5225$	$2$	5225.a	1.a	$1$	$2$	$2$	$41.722$	$\Q(\sqrt{2}) $	None	✓	$1$	$2$	$-2$	$-4$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots$
5225.2.a.e	$5225$	$2$	5225.a	1.a	$1$	$2$	$2$	$41.722$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$-4$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots$
5225.2.a.f	$5225$	$2$	5225.a	1.a	$1$	$2$	$2$	$41.722$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{3}+(-2+\beta )q^{6}+(2+\cdots)q^{7}+\cdots$
5225.2.a.g	$5225$	$2$	5225.a	1.a	$1$	$2$	$2$	$41.722$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$4$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+(2+\cdots)q^{6}+\cdots$
5225.2.a.h	$5225$	$2$	5225.a	1.a	$1$	$5$	$5$	$41.722$	5.5.246832.1	None	✓	$1$	$0$	$-2$	$-1$	$0$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots$
5225.2.a.i	$5225$	$2$	5225.a	1.a	$1$	$5$	$5$	$41.722$	5.5.36497.1	None	✓	$1$	$1$	$1$	$3$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(1-\beta _{1})q^{3}+\beta _{3}q^{4}+(-1+\cdots)q^{6}+\cdots$
5225.2.a.j	$5225$	$2$	5225.a	1.a	$1$	$5$	$5$	$41.722$	$\Q(\zeta_{22})^+$	None	✓	$1$	$0$	$3$	$7$	$0$	$11$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3}-\beta _{4})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
5225.2.a.k	$5225$	$2$	5225.a	1.a	$1$	$6$	$6$	$41.722$	6.6.131947641.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
5225.2.a.l	$5225$	$2$	5225.a	1.a	$1$	$6$	$6$	$41.722$	6.6.7281497.1	None	✓	$1$	$1$	$2$	$1$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(\beta _{4}+\beta _{5})q^{4}+\beta _{2}q^{6}+\cdots$
5225.2.a.m	$5225$	$2$	5225.a	1.a	$1$	$7$	$7$	$41.722$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-1$	$-3$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots$
5225.2.a.n	$5225$	$2$	5225.a	1.a	$1$	$7$	$7$	$41.722$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$1$	$-2$	$0$	$-10$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots$
5225.2.a.o	$5225$	$2$	5225.a	1.a	$1$	$8$	$8$	$41.722$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$6$	$7$	$0$	$11$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
5225.2.a.p	$5225$	$2$	5225.a	1.a	$1$	$9$	$9$	$41.722$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-3$	$-3$	$0$	$-13$	$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{6}+\cdots$
5225.2.a.q	$5225$	$2$	5225.a	1.a	$1$	$9$	$9$	$41.722$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-3$	$-3$	$0$	$9$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{1}-\beta _{8})q^{4}+\cdots$
5225.2.a.r	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-5$	$-4$	$0$	$-21$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots$
5225.2.a.s	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-5$	$-4$	$0$	$-15$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
5225.2.a.t	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$-1$	$4$	$0$	$11$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{6}+\cdots$
5225.2.a.u	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$-1$	$4$	$0$	$17$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{6}+\cdots$
5225.2.a.v	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$1$	$-4$	$0$	$-17$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{6}+\cdots$
5225.2.a.w	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$1$	$-4$	$0$	$-11$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{6}+\cdots$
5225.2.a.x	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$5$	$4$	$0$	$15$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
5225.2.a.y	$5225$	$2$	5225.a	1.a	$1$	$15$	$15$	$41.722$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$5$	$4$	$0$	$21$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots$
5225.2.a.z	$5225$	$2$	5225.a	1.a	$1$	$16$	$16$	$41.722$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}+(-1+\beta _{6}+\cdots)q^{6}+\cdots$
5225.2.a.ba	$5225$	$2$	5225.a	1.a	$1$	$20$	$20$	$41.722$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
5225.2.a.bb	$5225$	$2$	5225.a	1.a	$1$	$22$	$22$	$41.722$		None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
5225.2.a.bc	$5225$	$2$	5225.a	1.a	$1$	$30$	$30$	$41.722$		None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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