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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 (38 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4114.2.a.a	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+4q^{7}-q^{8}+\cdots$
4114.2.a.b	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$
4114.2.a.c	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}+2q^{13}+\cdots$
4114.2.a.d	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}-3q^{9}+\cdots$
4114.2.a.e	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-1$	$-1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+\beta q^{7}+\cdots$
4114.2.a.f	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots$
4114.2.a.g	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-1$	$2$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(2+\cdots)q^{7}+\cdots$
4114.2.a.h	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$1$	$-1$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
4114.2.a.i	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$3$	$-4$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots$
4114.2.a.j	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
4114.2.a.k	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots$
4114.2.a.l	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$2$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
4114.2.a.m	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$1$	$-1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+(2+\cdots)q^{7}+\cdots$
4114.2.a.n	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$3$	$-4$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots$
4114.2.a.o	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.321.1	None	✓	$1$	$1$	$-3$	$-1$	$-3$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
4114.2.a.p	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.257.1	None	✓	$1$	$1$	$-3$	$3$	$-1$	$-7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
4114.2.a.q	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.733.1	None	✓	$1$	$0$	$-3$	$3$	$2$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{1})q^{5}+\cdots$
4114.2.a.r	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.321.1	None	✓	$1$	$1$	$3$	$-1$	$-3$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
4114.2.a.s	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.785.1	None	✓	$1$	$1$	$3$	$-1$	$-1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
4114.2.a.t	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.733.1	None	✓	$1$	$0$	$3$	$3$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{1})q^{5}+\cdots$
4114.2.a.u	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.725.1	None	✓	$1$	$0$	$-4$	$-5$	$-6$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-2+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
4114.2.a.v	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.2525.1	None	✓	$1$	$0$	$-4$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{2}-\beta _{3})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
4114.2.a.w	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$1$	$1$	$-4$	$0$	$-6$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
4114.2.a.x	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.17417.1	None	✓	$1$	$0$	$-4$	$1$	$-1$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots$
4114.2.a.y	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.13676.1	None	✓	$1$	$0$	$-4$	$1$	$5$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}+(2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
4114.2.a.z	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.725.1	None	✓	$1$	$1$	$4$	$-5$	$-6$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-2+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
4114.2.a.ba	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.2525.1	None	✓	$1$	$1$	$4$	$-1$	$-2$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{2}-\beta _{3})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
4114.2.a.bb	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$1$	$1$	$4$	$0$	$-6$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
4114.2.a.bc	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.55585.1	None	✓	$1$	$0$	$4$	$1$	$5$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots$
4114.2.a.bd	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.13676.1	None	✓	$1$	$0$	$4$	$1$	$5$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
4114.2.a.be	$4114$	$2$	4114.a	1.a	$1$	$5$	$5$	$32.850$	5.5.7679496.1	None	✓	$1$	$0$	$-5$	$1$	$3$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
4114.2.a.bf	$4114$	$2$	4114.a	1.a	$1$	$5$	$5$	$32.850$	5.5.7679496.1	None	✓	$1$	$0$	$5$	$1$	$3$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
4114.2.a.bg	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$-5$	$2$	$-11$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{6}q^{5}+\cdots$
4114.2.a.bh	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$4$	$6$	$8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots$
4114.2.a.bi	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$-5$	$2$	$11$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{6}q^{5}+\cdots$
4114.2.a.bj	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$4$	$6$	$-8$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots$
4114.2.a.bk	$4114$	$2$	4114.a	1.a	$1$	$10$	$10$	$32.850$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$2$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$
4114.2.a.bl	$4114$	$2$	4114.a	1.a	$1$	$10$	$10$	$32.850$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$2$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$

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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.