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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 (46 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	13	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9802.2.a.a	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
9802.2.a.b	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$2$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{9}+2q^{14}+\cdots$
9802.2.a.c	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$3$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+3q^{7}+\cdots$
9802.2.a.d	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$0$	$1$	$-3$	$3$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}+3q^{5}-3q^{6}+2q^{7}+\cdots$
9802.2.a.e	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$2$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}-2q^{7}+\cdots$
9802.2.a.f	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}+2q^{14}+\cdots$
9802.2.a.g	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-3$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots$
9802.2.a.h	$9802$	$2$	9802.a	1.a	$1$	$1$	$1$	$78.269$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
9802.2.a.i	$9802$	$2$	9802.a	1.a	$1$	$2$	$2$	$78.269$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$-2$	$4$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots$
9802.2.a.j	$9802$	$2$	9802.a	1.a	$1$	$2$	$2$	$78.269$	$\Q(\sqrt{29}) $	None	✓	$1$	$0$	$-2$	$0$	$3$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+(2-\beta )q^{7}+\cdots$
9802.2.a.k	$9802$	$2$	9802.a	1.a	$1$	$2$	$2$	$78.269$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$2$	$1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-\beta )q^{5}-q^{6}+\cdots$
9802.2.a.l	$9802$	$2$	9802.a	1.a	$1$	$2$	$2$	$78.269$	$\Q(\sqrt{29}) $	None	✓	$1$	$1$	$2$	$0$	$-3$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
9802.2.a.m	$9802$	$2$	9802.a	1.a	$1$	$2$	$2$	$78.269$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$2$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
9802.2.a.n	$9802$	$2$	9802.a	1.a	$1$	$2$	$2$	$78.269$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$2$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+\beta q^{7}+\cdots$
9802.2.a.o	$9802$	$2$	9802.a	1.a	$1$	$3$	$3$	$78.269$	3.3.148.1	None	✓	$1$	$0$	$-3$	$1$	$1$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots$
9802.2.a.p	$9802$	$2$	9802.a	1.a	$1$	$3$	$3$	$78.269$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$3$	$2$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(2-2\beta _{1}+\cdots)q^{5}+\cdots$
9802.2.a.q	$9802$	$2$	9802.a	1.a	$1$	$3$	$3$	$78.269$	3.3.148.1	None	✓	$1$	$1$	$3$	$1$	$-1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
9802.2.a.r	$9802$	$2$	9802.a	1.a	$1$	$3$	$3$	$78.269$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$3$	$-2$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots$
9802.2.a.s	$9802$	$2$	9802.a	1.a	$1$	$4$	$4$	$78.269$	4.4.48528.1	None	✓	$1$	$0$	$-4$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
9802.2.a.t	$9802$	$2$	9802.a	1.a	$1$	$4$	$4$	$78.269$	4.4.27004.1	None	✓	$1$	$1$	$4$	$0$	$-7$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots$
9802.2.a.u	$9802$	$2$	9802.a	1.a	$1$	$4$	$4$	$78.269$	4.4.48528.1	None	✓	$1$	$1$	$4$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
9802.2.a.v	$9802$	$2$	9802.a	1.a	$1$	$4$	$4$	$78.269$	4.4.7232.1	None	✓	$1$	$0$	$4$	$2$	$2$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(\beta _{1}-2\beta _{3})q^{5}+\cdots$
9802.2.a.w	$9802$	$2$	9802.a	1.a	$1$	$5$	$5$	$78.269$	5.5.701089.1	None	✓	$1$	$0$	$-5$	$-2$	$5$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{4}q^{6}+\cdots$
9802.2.a.x	$9802$	$2$	9802.a	1.a	$1$	$5$	$5$	$78.269$	5.5.1220776.1	None	✓	$1$	$1$	$-5$	$3$	$-6$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
9802.2.a.y	$9802$	$2$	9802.a	1.a	$1$	$5$	$5$	$78.269$	5.5.701089.1	None	✓	$1$	$1$	$5$	$-2$	$-5$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{4}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots$
9802.2.a.z	$9802$	$2$	9802.a	1.a	$1$	$6$	$6$	$78.269$	6.6.226964648.1	None	✓	$1$	$0$	$-6$	$2$	$-3$	$1$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{2}q^{6}+\cdots$
9802.2.a.ba	$9802$	$2$	9802.a	1.a	$1$	$7$	$7$	$78.269$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$0$	$6$	$7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{6}q^{3}+q^{4}+(1-\beta _{2})q^{5}-\beta _{6}q^{6}+\cdots$
9802.2.a.bb	$9802$	$2$	9802.a	1.a	$1$	$7$	$7$	$78.269$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$7$	$0$	$-6$	$-7$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{6}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
9802.2.a.bc	$9802$	$2$	9802.a	1.a	$1$	$9$	$9$	$78.269$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$1$	$-6$	$-8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots$
9802.2.a.bd	$9802$	$2$	9802.a	1.a	$1$	$9$	$9$	$78.269$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$9$	$1$	$6$	$8$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots$
9802.2.a.be	$9802$	$2$	9802.a	1.a	$1$	$10$	$10$	$78.269$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$0$	$-4$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots$
9802.2.a.bf	$9802$	$2$	9802.a	1.a	$1$	$10$	$10$	$78.269$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$0$	$-4$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}+\beta _{1}q^{6}+\cdots$
9802.2.a.bg	$9802$	$2$	9802.a	1.a	$1$	$10$	$10$	$78.269$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-10$	$0$	$8$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots$
9802.2.a.bh	$9802$	$2$	9802.a	1.a	$1$	$10$	$10$	$78.269$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$10$	$0$	$-8$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots$
9802.2.a.bi	$9802$	$2$	9802.a	1.a	$1$	$10$	$10$	$78.269$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$0$	$4$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots$
9802.2.a.bj	$9802$	$2$	9802.a	1.a	$1$	$10$	$10$	$78.269$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$0$	$4$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots$
9802.2.a.bk	$9802$	$2$	9802.a	1.a	$1$	$18$	$18$	$78.269$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$-18$	$-10$	$4$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{8}q^{5}+\cdots$
9802.2.a.bl	$9802$	$2$	9802.a	1.a	$1$	$18$	$18$	$78.269$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$-18$	$5$	$-10$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{15})q^{5}+\cdots$
9802.2.a.bm	$9802$	$2$	9802.a	1.a	$1$	$18$	$18$	$78.269$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$18$	$-10$	$-4$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{8}q^{5}+\cdots$
9802.2.a.bn	$9802$	$2$	9802.a	1.a	$1$	$18$	$18$	$78.269$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$18$	$5$	$10$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{15})q^{5}+\cdots$
9802.2.a.bo	$9802$	$2$	9802.a	1.a	$1$	$20$	$20$	$78.269$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$-20$	$0$	$-12$	$-10$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{15})q^{5}+\cdots$
9802.2.a.bp	$9802$	$2$	9802.a	1.a	$1$	$20$	$20$	$78.269$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$20$	$0$	$12$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{15})q^{5}+\cdots$
9802.2.a.bq	$9802$	$2$	9802.a	1.a	$1$	$21$	$21$	$78.269$		None	✓	$1$	$1$	$-21$	$-11$	$8$	$7$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
9802.2.a.br	$9802$	$2$	9802.a	1.a	$1$	$21$	$21$	$78.269$		None	✓	$1$	$1$	$21$	$-11$	$-8$	$-7$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
9802.2.a.bs	$9802$	$2$	9802.a	1.a	$1$	$24$	$24$	$78.269$		None	✓	$1$	$0$	$-24$	$7$	$-4$	$-5$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
9802.2.a.bt	$9802$	$2$	9802.a	1.a	$1$	$24$	$24$	$78.269$		None	✓	$1$	$0$	$24$	$7$	$4$	$5$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.