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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 (40 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	3	353	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6354.2.a.a	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓	✓			6354.2.a.a	$1$	$1$	$-1$	$0$	$-2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
6354.2.a.b	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.e	$1$	$0$	$-1$	$0$	$-1$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
6354.2.a.c	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓	✓			6354.2.a.c	$1$	$2$	$-1$	$0$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{7}-q^{8}-6q^{11}-7q^{13}+\cdots$
6354.2.a.d	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.h	$1$	$1$	$-1$	$0$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{7}-q^{8}+6q^{11}-q^{13}+\cdots$
6354.2.a.e	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				706.2.a.b	$1$	$0$	$-1$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+4q^{11}-4q^{13}+\cdots$
6354.2.a.f	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓	✓			6354.2.a.f	$1$	$1$	$-1$	$0$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{7}-q^{8}+2q^{11}-5q^{13}+\cdots$
6354.2.a.g	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				706.2.a.d	$1$	$0$	$-1$	$0$	$1$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
6354.2.a.h	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.g	$1$	$1$	$-1$	$0$	$2$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots$
6354.2.a.i	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.d	$1$	$0$	$-1$	$0$	$2$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
6354.2.a.j	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.f	$1$	$1$	$-1$	$0$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}-4q^{13}+\cdots$
6354.2.a.k	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				706.2.a.c	$1$	$0$	$-1$	$0$	$4$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+2q^{7}-q^{8}-4q^{10}+\cdots$
6354.2.a.l	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.c	$1$	$2$	$1$	$0$	$-4$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}-5q^{7}+q^{8}-4q^{10}+\cdots$
6354.2.a.m	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.b	$1$	$0$	$1$	$0$	$-3$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots$
6354.2.a.n	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				2118.2.a.a	$1$	$1$	$1$	$0$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
6354.2.a.o	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓	✓			6354.2.a.c	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{7}+q^{8}+6q^{11}-7q^{13}+\cdots$
6354.2.a.p	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓	✓			6354.2.a.f	$1$	$1$	$1$	$0$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{7}+q^{8}-2q^{11}-5q^{13}+\cdots$
6354.2.a.q	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓	✓			6354.2.a.a	$1$	$1$	$1$	$0$	$2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
6354.2.a.r	$6354$	$2$	6354.a	1.a	$1$	$1$	$1$	$50.737$	$\Q$	None	✓				706.2.a.a	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+q^{11}+\cdots$
6354.2.a.s	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{2}) $	None	✓				706.2.a.e	$1$	$1$	$-2$	$0$	$-4$	$8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{5}+4q^{7}-q^{8}+\cdots$
6354.2.a.t	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{13}) $	None	✓	✓			6354.2.a.t	$1$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+(-1-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
6354.2.a.u	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{3}) $	None	✓				2118.2.a.m	$1$	$0$	$-2$	$0$	$0$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(3+\beta )q^{7}-q^{8}+\cdots$
6354.2.a.v	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{5}) $	None	✓				2118.2.a.i	$1$	$1$	$2$	$0$	$-2$	$-6$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{5}-3q^{7}+q^{8}+\cdots$
6354.2.a.w	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{5}) $	None	✓				2118.2.a.j	$1$	$1$	$2$	$0$	$-2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2\beta q^{5}+2\beta q^{7}+q^{8}+\cdots$
6354.2.a.x	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{2}) $	None	✓				2118.2.a.l	$1$	$1$	$2$	$0$	$0$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}-3q^{7}+q^{8}+\beta q^{10}+\cdots$
6354.2.a.y	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{13}) $	None	✓	✓			6354.2.a.t	$1$	$1$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+(1+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
6354.2.a.z	$6354$	$2$	6354.a	1.a	$1$	$2$	$2$	$50.737$	$\Q(\sqrt{2}) $	None	✓				2118.2.a.k	$1$	$1$	$2$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}-\beta q^{7}+q^{8}+\cdots$
6354.2.a.ba	$6354$	$2$	6354.a	1.a	$1$	$3$	$3$	$50.737$	3.3.1436.1	None	✓				2118.2.a.p	$1$	$0$	$-3$	$0$	$-4$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots$
6354.2.a.bb	$6354$	$2$	6354.a	1.a	$1$	$3$	$3$	$50.737$	3.3.961.1	None	✓				2118.2.a.o	$1$	$0$	$-3$	$0$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots$
6354.2.a.bc	$6354$	$2$	6354.a	1.a	$1$	$3$	$3$	$50.737$	3.3.148.1	None	✓				2118.2.a.n	$1$	$0$	$-3$	$0$	$3$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
6354.2.a.bd	$6354$	$2$	6354.a	1.a	$1$	$5$	$5$	$50.737$	5.5.934448.1	None	✓	✓	✓		6354.2.a.bd	$1$	$1$	$-5$	$0$	$7$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
6354.2.a.be	$6354$	$2$	6354.a	1.a	$1$	$5$	$5$	$50.737$	5.5.934448.1	None	✓	✓	✓		6354.2.a.bd	$1$	$1$	$5$	$0$	$-7$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
6354.2.a.bf	$6354$	$2$	6354.a	1.a	$1$	$5$	$5$	$50.737$	5.5.126032.1	None	✓				706.2.a.f	$1$	$0$	$5$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{5}+\cdots$
6354.2.a.bg	$6354$	$2$	6354.a	1.a	$1$	$6$	$6$	$50.737$	6.6.55540832.1	None	✓				2118.2.a.q	$1$	$1$	$-6$	$0$	$-2$	$6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
6354.2.a.bh	$6354$	$2$	6354.a	1.a	$1$	$7$	$7$	$50.737$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		2118.2.a.r	$1$	$0$	$-7$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{4}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\cdots$
6354.2.a.bi	$6354$	$2$	6354.a	1.a	$1$	$8$	$8$	$50.737$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		706.2.a.g	$1$	$1$	$8$	$0$	$-5$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
6354.2.a.bj	$6354$	$2$	6354.a	1.a	$1$	$9$	$9$	$50.737$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				2118.2.a.s	$1$	$0$	$9$	$0$	$4$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{8}+\cdots$
6354.2.a.bk	$6354$	$2$	6354.a	1.a	$1$	$10$	$10$	$50.737$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		706.2.a.h	$1$	$1$	$-10$	$0$	$-3$	$-12$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{1}+\beta _{6}-\beta _{8}+\beta _{9})q^{5}+\cdots$
6354.2.a.bl	$6354$	$2$	6354.a	1.a	$1$	$10$	$10$	$50.737$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		2118.2.a.t	$1$	$0$	$10$	$0$	$10$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{9})q^{5}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
6354.2.a.bm	$6354$	$2$	6354.a	1.a	$1$	$20$	$20$	$50.737$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	✓	✓		6354.2.a.bm	$1$	$0$	$-20$	$0$	$-5$	$11$	$+$	$+$	$-$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(1-\beta _{2})q^{7}-q^{8}+\cdots$
6354.2.a.bn	$6354$	$2$	6354.a	1.a	$1$	$20$	$20$	$50.737$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	✓	✓		6354.2.a.bm	$1$	$0$	$20$	$0$	$5$	$11$	$-$	$+$	$+$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{8}+\cdots$

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