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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 (29 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2768.1.g.a	$2768$	$1$	2768.g	692.d	$2$	$1$	$1$	$1.381$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-173}) $	$\Q(\sqrt{173}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{9}+2q^{13}+q^{25}-2q^{29}+2q^{37}+\cdots$
2768.1.g.b	$2768$	$1$	2768.g	692.d	$2$	$6$	$6$	$1.381$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-173}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{2})q^{9}+\beta _{5}q^{11}+\cdots$
2768.1.j.a	$2768$	$1$	2768.j	2768.j	$4$	$2$	$1$	$1.381$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$-2$	$0$	$2$	$-2$		$1$		$q-q^{2}+iq^{3}+q^{4}+q^{5}-iq^{6}+(-1+\cdots)q^{7}+\cdots$
2768.1.j.b	$2768$	$1$	2768.j	2768.j	$4$	$2$	$1$	$1.381$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}+iq^{8}+\cdots$
2768.1.k.a	$2768$	$1$	2768.k	2768.k	$4$	$4$	$2$	$1.381$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
2768.1.k.b	$2768$	$1$	2768.k	2768.k	$4$	$4$	$2$	$1.381$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
2768.1.s.a	$2768$	$1$	2768.s	2768.s	$4$	$2$	$1$	$1.381$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-iq^{5}-q^{6}-q^{8}+\cdots$
2768.1.s.b	$2768$	$1$	2768.s	2768.s	$4$	$2$	$1$	$1.381$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$0$	$2$		$1$		$q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+(1+\cdots)q^{7}+\cdots$
2768.1.w.a	$2768$	$1$	2768.w	692.h	$86$	$42$	$1$	$1.381$	$\Q(\zeta_{86})$	$D_{86}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{86}^{2}+\zeta_{86}^{23})q^{5}-\zeta_{86}^{14}q^{9}+\cdots$
2768.2.a.a	$2768$	$2$	2768.a	1.a	$1$	$1$	$1$	$22.103$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-3$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}+6q^{9}-4q^{11}-2q^{13}+\cdots$
2768.2.a.b	$2768$	$2$	2768.a	1.a	$1$	$1$	$1$	$22.103$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}-2q^{9}-4q^{11}+\cdots$
2768.2.a.c	$2768$	$2$	2768.a	1.a	$1$	$1$	$1$	$22.103$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots$
2768.2.a.d	$2768$	$2$	2768.a	1.a	$1$	$1$	$1$	$22.103$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
2768.2.a.e	$2768$	$2$	2768.a	1.a	$1$	$3$	$3$	$22.103$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
2768.2.a.f	$2768$	$2$	2768.a	1.a	$1$	$4$	$4$	$22.103$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1-\beta _{1}+\beta _{3})q^{7}+\cdots$
2768.2.a.g	$2768$	$2$	2768.a	1.a	$1$	$4$	$4$	$22.103$	4.4.2777.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}+\beta _{3})q^{3}+(-2+\beta _{1}+\beta _{3})q^{5}+\cdots$
2768.2.a.h	$2768$	$2$	2768.a	1.a	$1$	$4$	$4$	$22.103$	4.4.725.1	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$-1$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{2})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
2768.2.a.i	$2768$	$2$	2768.a	1.a	$1$	$5$	$5$	$22.103$	5.5.2075621.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{2}-\beta _{4})q^{5}-\beta _{4}q^{7}+\cdots$
2768.2.a.j	$2768$	$2$	2768.a	1.a	$1$	$8$	$8$	$22.103$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
2768.2.a.k	$2768$	$2$	2768.a	1.a	$1$	$10$	$10$	$22.103$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$1$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}+\beta _{9}q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots$
2768.2.a.l	$2768$	$2$	2768.a	1.a	$1$	$10$	$10$	$22.103$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$3$	$-13$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{8})q^{7}+(1+\cdots)q^{9}+\cdots$
2768.2.a.m	$2768$	$2$	2768.a	1.a	$1$	$10$	$10$	$22.103$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{7})q^{5}+(-1+\cdots)q^{7}+\cdots$
2768.2.a.n	$2768$	$2$	2768.a	1.a	$1$	$11$	$11$	$22.103$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$13$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(2-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
2768.2.a.o	$2768$	$2$	2768.a	1.a	$1$	$13$	$13$	$22.103$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$10$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{5})q^{5}+(1-\beta _{9})q^{7}+\cdots$
2768.2.b.a	$2768$	$2$	2768.b	173.b	$2$	$2$	$2$	$22.103$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+3iq^{5}-2iq^{7}+2q^{9}+4q^{13}+\cdots$
2768.2.b.b	$2768$	$2$	2768.b	173.b	$2$	$12$	$12$	$22.103$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{9})q^{3}+(\beta _{3}+\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
2768.2.b.c	$2768$	$2$	2768.b	173.b	$2$	$14$	$14$	$22.103$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}-\beta _{8}q^{5}+\beta _{9}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
2768.2.b.d	$2768$	$2$	2768.b	173.b	$2$	$14$	$14$	$22.103$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
2768.2.b.e	$2768$	$2$	2768.b	173.b	$2$	$44$	$44$	$22.103$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.