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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 (41 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
1328.1.g.a	$1328$	$1$	1328.g	83.b	$2$	$1$	$1$	$0.663$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+q^{3}+q^{7}+q^{11}-q^{17}+q^{21}-2q^{23}+\cdots$
1328.1.g.b	$1328$	$1$	1328.g	83.b	$2$	$3$	$3$	$0.663$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
1328.2.a.a	$1328$	$2$	1328.a	1.a	$1$	$1$	$1$	$10.604$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots$
1328.2.a.b	$1328$	$2$	1328.a	1.a	$1$	$1$	$1$	$10.604$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}-2q^{9}+5q^{11}+\cdots$
1328.2.a.c	$1328$	$2$	1328.a	1.a	$1$	$1$	$1$	$10.604$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+3q^{7}-2q^{9}-3q^{11}+\cdots$
1328.2.a.d	$1328$	$2$	1328.a	1.a	$1$	$1$	$1$	$10.604$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots$
1328.2.a.e	$1328$	$2$	1328.a	1.a	$1$	$1$	$1$	$10.604$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{5}+5q^{7}+6q^{9}+3q^{11}+\cdots$
1328.2.a.f	$1328$	$2$	1328.a	1.a	$1$	$2$	$2$	$10.604$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}-\beta q^{7}+4q^{9}+\cdots$
1328.2.a.g	$1328$	$2$	1328.a	1.a	$1$	$2$	$2$	$10.604$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+(3-\beta )q^{7}+2\beta q^{9}+\cdots$
1328.2.a.h	$1328$	$2$	1328.a	1.a	$1$	$2$	$2$	$10.604$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1328.2.a.i	$1328$	$2$	1328.a	1.a	$1$	$3$	$3$	$10.604$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$2$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}-2\beta _{2}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$
1328.2.a.j	$1328$	$2$	1328.a	1.a	$1$	$3$	$3$	$10.604$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
1328.2.a.k	$1328$	$2$	1328.a	1.a	$1$	$4$	$4$	$10.604$	4.4.2225.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-5$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+\beta _{1}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
1328.2.a.l	$1328$	$2$	1328.a	1.a	$1$	$6$	$6$	$10.604$	6.6.9059636.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots$
1328.2.a.m	$1328$	$2$	1328.a	1.a	$1$	$6$	$6$	$10.604$	6.6.905177.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-4$	$5$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1+\beta _{2}+\beta _{3})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
1328.2.a.n	$1328$	$2$	1328.a	1.a	$1$	$8$	$8$	$10.604$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$7$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{7})q^{5}+\beta _{2}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots$
1328.2.b.a	$1328$	$2$	1328.b	332.b	$2$	$6$	$6$	$10.604$	6.0.416832723.1	$_{}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{7}+(-3+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
1328.2.b.b	$1328$	$2$	1328.b	332.b	$2$	$8$	$8$	$10.604$	8.0.$\cdots$.50	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(\beta _{2}+2\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots$
1328.2.b.c	$1328$	$2$	1328.b	332.b	$2$	$12$	$12$	$10.604$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{6}q^{3}-\beta _{7}q^{7}+(-3-\beta _{11})q^{9}+\cdots$
1328.2.b.d	$1328$	$2$	1328.b	332.b	$2$	$16$	$16$	$10.604$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+\beta _{13}q^{9}+\cdots$
1328.3.d.a	$1328$	$3$	1328.d	4.b	$2$	$26$	$26$	$36.185$		$_{}$	None	None		$2$	$0$	$0$	$0$	$16$	$0$			$\mathrm{SU}(2)[C_{2}]$
1328.3.d.b	$1328$	$3$	1328.d	4.b	$2$	$56$	$56$	$36.185$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
1328.3.g.a	$1328$	$3$	1328.g	83.b	$2$	$3$	$3$	$36.185$	3.3.2241.1	$_{}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-\beta _{2})q^{3}+(3\beta _{1}+2\beta _{2})q^{7}+\cdots$
1328.3.g.b	$1328$	$3$	1328.g	83.b	$2$	$6$	$6$	$36.185$	6.6.$\cdots$.2	$_{}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{3}+(-2\beta _{2}+\beta _{3}-2\beta _{4})q^{7}+\cdots$
1328.3.g.c	$1328$	$3$	1328.g	83.b	$2$	$8$	$8$	$36.185$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}+\beta _{1}q^{5}+(1-\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots$
1328.3.g.d	$1328$	$3$	1328.g	83.b	$2$	$10$	$10$	$36.185$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$-12$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{3}+\beta _{6}q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots$
1328.3.g.e	$1328$	$3$	1328.g	83.b	$2$	$14$	$14$	$36.185$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$20$		$2^{5}\cdot 3^{5}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1-\beta _{5})q^{7}+(4-\beta _{2}+\cdots)q^{9}+\cdots$
1328.3.g.f	$1328$	$3$	1328.g	83.b	$2$	$42$	$42$	$36.185$		$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1328.4.a.a	$1328$	$4$	1328.a	1.a	$1$	$1$	$1$	$78.355$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$8$	$31$	$+$	$1$	$\mathrm{SU}(2)$	$q+5q^{3}+8q^{5}+31q^{7}-2q^{9}-3q^{11}+\cdots$
1328.4.a.b	$1328$	$4$	1328.a	1.a	$1$	$2$	$2$	$78.355$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-24$	$6$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-12+\beta )q^{5}+(3-7\beta )q^{7}+\cdots$
1328.4.a.c	$1328$	$4$	1328.a	1.a	$1$	$5$	$5$	$78.355$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-22$	$-14$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{3}+(-4+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{5}+\cdots$
1328.4.a.d	$1328$	$4$	1328.a	1.a	$1$	$6$	$6$	$78.355$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$14$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1+\beta _{4})q^{5}+(2-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1328.4.a.e	$1328$	$4$	1328.a	1.a	$1$	$7$	$7$	$78.355$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$9$	$-33$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots$
1328.4.a.f	$1328$	$4$	1328.a	1.a	$1$	$7$	$7$	$78.355$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$11$	$-17$	$46$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(2+\beta _{1})q^{3}+(-2+\beta _{1}+\beta _{2}-\beta _{6})q^{5}+\cdots$
1328.4.a.g	$1328$	$4$	1328.a	1.a	$1$	$9$	$9$	$78.355$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$-1$	$57$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+(6+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
1328.4.a.h	$1328$	$4$	1328.a	1.a	$1$	$12$	$12$	$78.355$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-10$	$-1$	$-41$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+\beta _{8}q^{5}+(-3-\beta _{3}+\cdots)q^{7}+\cdots$
1328.4.a.i	$1328$	$4$	1328.a	1.a	$1$	$12$	$12$	$78.355$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-7$	$-4$	$-$	$2^{9}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1328.4.a.j	$1328$	$4$	1328.a	1.a	$1$	$13$	$13$	$78.355$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-7$	$33$	$-52$	$+$	$2^{10}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{6})q^{3}+(3+\beta _{9})q^{5}+(-4+\cdots)q^{7}+\cdots$
1328.4.a.k	$1328$	$4$	1328.a	1.a	$1$	$14$	$14$	$78.355$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-9$	$14$	$-27$	$-$	$2^{12}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1+\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots$
1328.4.a.l	$1328$	$4$	1328.a	1.a	$1$	$16$	$16$	$78.355$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$-11$	$43$	$+$	$2^{16}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(3+\beta _{12}+\cdots)q^{7}+\cdots$
1328.4.a.m	$1328$	$4$	1328.a	1.a	$1$	$19$	$19$	$78.355$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$18$	$24$	$+$	$2^{18}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(1+\beta _{13})q^{7}+\cdots$

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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.