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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 (38 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
4338.2.a.a	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.g	$1$	$1$	$-1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots$
4338.2.a.b	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.f	$1$	$0$	$-1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots$
4338.2.a.c	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.e	$1$	$0$	$-1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+4q^{7}-q^{8}-2q^{10}+\cdots$
4338.2.a.d	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.c	$1$	$1$	$1$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots$
4338.2.a.e	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.d	$1$	$1$	$1$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots$
4338.2.a.f	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				482.2.a.a	$1$	$1$	$1$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
4338.2.a.g	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.a	$1$	$0$	$1$	$0$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-5q^{7}+q^{8}+3q^{10}+\cdots$
4338.2.a.h	$4338$	$2$	4338.a	1.a	$1$	$1$	$1$	$34.639$	$\Q$	None	✓				1446.2.a.b	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots$
4338.2.a.i	$4338$	$2$	4338.a	1.a	$1$	$2$	$2$	$34.639$	$\Q(\sqrt{2}) $	None	✓				1446.2.a.j	$1$	$1$	$-2$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+(-2+\beta )q^{7}+\cdots$
4338.2.a.j	$4338$	$2$	4338.a	1.a	$1$	$2$	$2$	$34.639$	$\Q(\sqrt{2}) $	None	✓				1446.2.a.i	$1$	$1$	$-2$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1+\beta )q^{7}-q^{8}+\cdots$
4338.2.a.k	$4338$	$2$	4338.a	1.a	$1$	$2$	$2$	$34.639$	$\Q(\sqrt{5}) $	None	✓				482.2.a.b	$1$	$1$	$-2$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+(-3+2\beta )q^{7}+\cdots$
4338.2.a.l	$4338$	$2$	4338.a	1.a	$1$	$2$	$2$	$34.639$	$\Q(\sqrt{2}) $	None	✓				1446.2.a.h	$1$	$1$	$2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
4338.2.a.m	$4338$	$2$	4338.a	1.a	$1$	$3$	$3$	$34.639$	3.3.148.1	None	✓	✓			4338.2.a.m	$1$	$0$	$-3$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
4338.2.a.n	$4338$	$2$	4338.a	1.a	$1$	$3$	$3$	$34.639$	3.3.148.1	None	✓	✓			4338.2.a.m	$1$	$1$	$3$	$0$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
4338.2.a.o	$4338$	$2$	4338.a	1.a	$1$	$3$	$3$	$34.639$	3.3.229.1	None	✓				482.2.a.c	$1$	$1$	$3$	$0$	$-2$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}-3q^{7}+\cdots$
4338.2.a.p	$4338$	$2$	4338.a	1.a	$1$	$3$	$3$	$34.639$	3.3.148.1	None	✓				1446.2.a.k	$1$	$1$	$3$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+2\beta _{2}q^{7}+\cdots$
4338.2.a.q	$4338$	$2$	4338.a	1.a	$1$	$4$	$4$	$34.639$	4.4.7168.1	None	✓	✓	✓		4338.2.a.q	$1$	$0$	$-4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$
4338.2.a.r	$4338$	$2$	4338.a	1.a	$1$	$4$	$4$	$34.639$	4.4.7168.1	None	✓	✓	✓		4338.2.a.q	$1$	$1$	$4$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots$
4338.2.a.s	$4338$	$2$	4338.a	1.a	$1$	$4$	$4$	$34.639$	4.4.11348.1	None	✓				1446.2.a.l	$1$	$0$	$4$	$0$	$1$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+(-1+\beta _{2}-\beta _{3})q^{7}+\cdots$
4338.2.a.t	$4338$	$2$	4338.a	1.a	$1$	$5$	$5$	$34.639$	5.5.1455344.1	None	✓				1446.2.a.m	$1$	$0$	$-5$	$0$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
4338.2.a.u	$4338$	$2$	4338.a	1.a	$1$	$6$	$6$	$34.639$	6.6.131357120.1	None	✓				482.2.a.d	$1$	$0$	$6$	$0$	$5$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{5})q^{5}+(2+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
4338.2.a.v	$4338$	$2$	4338.a	1.a	$1$	$7$	$7$	$34.639$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1446.2.a.o	$1$	$1$	$-7$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots$
4338.2.a.w	$4338$	$2$	4338.a	1.a	$1$	$7$	$7$	$34.639$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		1446.2.a.n	$1$	$0$	$7$	$0$	$-5$	$7$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{3})q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots$
4338.2.a.x	$4338$	$2$	4338.a	1.a	$1$	$9$	$9$	$34.639$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓		✓		482.2.a.e	$1$	$0$	$-9$	$0$	$-5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{4})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
4338.2.a.y	$4338$	$2$	4338.a	1.a	$1$	$13$	$13$	$34.639$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	4338.2.a.y	$1$	$1$	$-13$	$0$	$-4$	$-2$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{8}q^{5}-\beta _{7}q^{7}-q^{8}+\cdots$
4338.2.a.z	$4338$	$2$	4338.a	1.a	$1$	$13$	$13$	$34.639$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	4338.2.a.y	$1$	$0$	$13$	$0$	$4$	$-2$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{8}q^{5}-\beta _{7}q^{7}+q^{8}+\cdots$
4338.2.d.a	$4338$	$2$	4338.d	241.b	$2$	$2$	$2$	$34.639$	$\Q(\sqrt{-6}) $	None					1446.2.d.c	$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-q^{8}+2\beta q^{11}-\beta q^{13}+\cdots$
4338.2.d.b	$4338$	$2$	4338.d	241.b	$2$	$2$	$2$	$34.639$	$\Q(\sqrt{-2}) $	None					1446.2.d.b	$2$	$1$	$2$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-4q^{5}+2\beta q^{7}+q^{8}-4q^{10}+\cdots$
4338.2.d.c	$4338$	$2$	4338.d	241.b	$2$	$2$	$2$	$34.639$	$\Q(\sqrt{-1}) $	None					1446.2.d.a	$2$	$0$	$2$	$0$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+3q^{5}-iq^{7}+q^{8}+3q^{10}+\cdots$
4338.2.d.d	$4338$	$2$	4338.d	241.b	$2$	$4$	$4$	$34.639$	4.0.8112.1	None					482.2.b.a	$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{7}+q^{8}+\cdots$
4338.2.d.e	$4338$	$2$	4338.d	241.b	$2$	$6$	$6$	$34.639$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None					1446.2.d.d	$2$	$0$	$6$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{4}q^{7}+q^{8}-\beta _{5}q^{11}+\cdots$
4338.2.d.f	$4338$	$2$	4338.d	241.b	$2$	$8$	$8$	$34.639$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None					1446.2.d.f	$2$	$0$	$-8$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{4}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots$
4338.2.d.g	$4338$	$2$	4338.d	241.b	$2$	$8$	$8$	$34.639$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None					1446.2.d.e	$2$	$0$	$8$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{5}q^{5}+\beta _{6}q^{7}+q^{8}+\cdots$
4338.2.d.h	$4338$	$2$	4338.d	241.b	$2$	$8$	$8$	$34.639$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None					482.2.b.b	$2$	$0$	$8$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{7}+q^{8}+\cdots$
4338.2.d.i	$4338$	$2$	4338.d	241.b	$2$	$10$	$10$	$34.639$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					1446.2.d.g	$2$	$0$	$-10$	$0$	$-2$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{2}q^{5}-\beta _{4}q^{7}-q^{8}+\cdots$
4338.2.d.j	$4338$	$2$	4338.d	241.b	$2$	$10$	$10$	$34.639$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					482.2.b.c	$2$	$0$	$-10$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{4}q^{5}+(\beta _{1}+\beta _{6})q^{7}+\cdots$
4338.2.d.k	$4338$	$2$	4338.d	241.b	$2$	$20$	$20$	$34.639$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			4338.2.d.k	$2$	$0$	$-20$	$0$	$-4$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{2}q^{5}+\beta _{18}q^{7}-q^{8}+\cdots$
4338.2.d.l	$4338$	$2$	4338.d	241.b	$2$	$20$	$20$	$34.639$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓			4338.2.d.k	$2$	$0$	$20$	$0$	$4$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{2}q^{5}-\beta _{18}q^{7}+q^{8}+\cdots$

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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.