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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 (23 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	11	43	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5203.2.a.a	$5203$	$2$	5203.a	1.a	$1$	$1$	$1$	$41.546$	$\Q$	None	✓	$1$	$1$	$2$	$-2$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}-4q^{5}-4q^{6}+\cdots$
5203.2.a.b	$5203$	$2$	5203.a	1.a	$1$	$1$	$1$	$41.546$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{9}+\cdots$
5203.2.a.c	$5203$	$2$	5203.a	1.a	$1$	$2$	$2$	$41.546$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$2$	$4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}-q^{4}+(2+\beta )q^{5}+\cdots$
5203.2.a.d	$5203$	$2$	5203.a	1.a	$1$	$2$	$2$	$41.546$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-4$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-2q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$
5203.2.a.e	$5203$	$2$	5203.a	1.a	$1$	$2$	$2$	$41.546$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$-2$	$2$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+2\beta q^{5}+\cdots$
5203.2.a.f	$5203$	$2$	5203.a	1.a	$1$	$2$	$2$	$41.546$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+(2+\beta )q^{5}+2q^{6}+(2+\cdots)q^{7}+\cdots$
5203.2.a.g	$5203$	$2$	5203.a	1.a	$1$	$2$	$2$	$41.546$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta )q^{3}-q^{4}+(2-\beta )q^{5}+\cdots$
5203.2.a.h	$5203$	$2$	5203.a	1.a	$1$	$5$	$5$	$41.546$	5.5.38569.1	None	✓	$1$	$1$	$-1$	$-3$	$-6$	$15$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}-\beta _{4})q^{3}+\cdots$
5203.2.a.i	$5203$	$2$	5203.a	1.a	$1$	$5$	$5$	$41.546$	5.5.173513.1	None	✓	$1$	$0$	$3$	$-1$	$-4$	$9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+\cdots$
5203.2.a.j	$5203$	$2$	5203.a	1.a	$1$	$9$	$9$	$41.546$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-4$	$5$	$0$	$-19$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
5203.2.a.k	$5203$	$2$	5203.a	1.a	$1$	$11$	$11$	$41.546$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$1$	$6$	$3$	$-17$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{8})q^{3}+(1+\beta _{2})q^{4}+\cdots$
5203.2.a.l	$5203$	$2$	5203.a	1.a	$1$	$15$	$15$	$41.546$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-2$	$-3$	$-3$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
5203.2.a.m	$5203$	$2$	5203.a	1.a	$1$	$15$	$15$	$41.546$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$2$	$-3$	$-3$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
5203.2.a.n	$5203$	$2$	5203.a	1.a	$1$	$17$	$17$	$41.546$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$1$	$-6$	$-1$	$1$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
5203.2.a.o	$5203$	$2$	5203.a	1.a	$1$	$17$	$17$	$41.546$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	None	✓	$1$	$0$	$6$	$-1$	$1$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
5203.2.a.p	$5203$	$2$	5203.a	1.a	$1$	$18$	$18$	$41.546$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$-5$	$-1$	$1$	$-4$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
5203.2.a.q	$5203$	$2$	5203.a	1.a	$1$	$18$	$18$	$41.546$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$5$	$-1$	$1$	$4$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
5203.2.a.r	$5203$	$2$	5203.a	1.a	$1$	$36$	$36$	$41.546$		None	✓	$1$	$1$	$-10$	$-2$	$-4$	$-8$	$+$	$+$	$+$		$\mathrm{SU}(2)$
5203.2.a.s	$5203$	$2$	5203.a	1.a	$1$	$36$	$36$	$41.546$		None	✓	$1$	$0$	$10$	$-2$	$-4$	$8$	$+$	$-$	$-$		$\mathrm{SU}(2)$
5203.2.a.t	$5203$	$2$	5203.a	1.a	$1$	$38$	$38$	$41.546$		None	✓	$1$	$1$	$0$	$-10$	$-26$	$2$	$-$	$-$	$+$		$\mathrm{SU}(2)$
5203.2.a.u	$5203$	$2$	5203.a	1.a	$1$	$38$	$38$	$41.546$		None	✓	$1$	$1$	$0$	$-10$	$-26$	$-2$	$+$	$+$	$+$		$\mathrm{SU}(2)$
5203.2.a.v	$5203$	$2$	5203.a	1.a	$1$	$46$	$46$	$41.546$		None	✓	$1$	$0$	$0$	$14$	$30$	$2$	$-$	$+$	$-$		$\mathrm{SU}(2)$
5203.2.a.w	$5203$	$2$	5203.a	1.a	$1$	$46$	$46$	$41.546$		None	✓	$1$	$0$	$0$	$14$	$30$	$-2$	$+$	$-$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
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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.