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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 (31 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
1012.1.r.a	$1012$	$1$	1012.r	253.k	$22$	$20$	$2$	$0.505$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$2$	$0$		$1$		$q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots$
1012.2.a.a	$1012$	$2$	1012.a	1.a	$1$	$1$	$1$	$8.081$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{7}-3q^{9}+q^{11}+2q^{13}+\cdots$
1012.2.a.b	$1012$	$2$	1012.a	1.a	$1$	$1$	$1$	$8.081$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots$
1012.2.a.c	$1012$	$2$	1012.a	1.a	$1$	$1$	$1$	$8.081$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}-2q^{9}-q^{11}+5q^{13}+\cdots$
1012.2.a.d	$1012$	$2$	1012.a	1.a	$1$	$1$	$1$	$8.081$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots$
1012.2.a.e	$1012$	$2$	1012.a	1.a	$1$	$3$	$3$	$8.081$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+\cdots$
1012.2.a.f	$1012$	$2$	1012.a	1.a	$1$	$3$	$3$	$8.081$	3.3.321.1	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots$
1012.2.a.g	$1012$	$2$	1012.a	1.a	$1$	$4$	$4$	$8.081$	4.4.2777.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1012.2.a.h	$1012$	$2$	1012.a	1.a	$1$	$4$	$4$	$8.081$	4.4.35537.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$5$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{5}+(-1-\beta _{3})q^{7}+\cdots$
1012.2.g.a	$1012$	$2$	1012.g	253.b	$2$	$4$	$4$	$8.081$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots$
1012.2.g.b	$1012$	$2$	1012.g	253.b	$2$	$20$	$20$	$8.081$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{5}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{18}q^{5}-\beta _{15}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots$
1012.2.i.a	$1012$	$2$	1012.i	11.c	$5$	$4$	$1$	$8.081$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
1012.2.i.b	$1012$	$2$	1012.i	11.c	$5$	$4$	$1$	$8.081$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$5$	$9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+2\zeta_{10}+\cdots)q^{5}+\cdots$
1012.2.i.c	$1012$	$2$	1012.i	11.c	$5$	$4$	$1$	$8.081$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}+\cdots)q^{5}+\cdots$
1012.2.i.d	$1012$	$2$	1012.i	11.c	$5$	$36$	$9$	$8.081$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$-10$			$\mathrm{SU}(2)[C_{5}]$
1012.2.i.e	$1012$	$2$	1012.i	11.c	$5$	$40$	$10$	$8.081$		$_{}$	None	None		$2$	$0$	$0$	$3$	$-5$	$3$			$\mathrm{SU}(2)[C_{5}]$
1012.2.k.a	$1012$	$2$	1012.k	253.h	$10$	$96$	$24$	$8.081$		$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1012.3.f.a	$1012$	$3$	1012.f	23.b	$2$	$40$	$40$	$27.575$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1012.3.h.a	$1012$	$3$	1012.h	11.b	$2$	$44$	$44$	$27.575$		$_{}$	None	None		$2$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1012.4.a.a	$1012$	$4$	1012.a	1.a	$1$	$13$	$13$	$59.710$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-9$	$-25$	$-40$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{6})q^{5}+(-3+\cdots)q^{7}+\cdots$
1012.4.a.b	$1012$	$4$	1012.a	1.a	$1$	$13$	$13$	$59.710$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-15$	$28$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{8})q^{5}+(2-\beta _{1}+\beta _{6}+\cdots)q^{7}+\cdots$
1012.4.a.c	$1012$	$4$	1012.a	1.a	$1$	$14$	$14$	$59.710$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-9$	$25$	$24$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(2+\beta _{3})q^{5}+(2-\beta _{5}+\cdots)q^{7}+\cdots$
1012.4.a.d	$1012$	$4$	1012.a	1.a	$1$	$14$	$14$	$59.710$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$35$	$20$	$+$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(3-\beta _{3})q^{5}+(1+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
1012.4.g.a	$1012$	$4$	1012.g	253.b	$2$	$4$	$4$	$59.710$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-16$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-4-\beta _{1}-\beta _{3})q^{3}+(-9-2\beta _{1}+\cdots)q^{5}+\cdots$
1012.4.g.b	$1012$	$4$	1012.g	253.b	$2$	$68$	$68$	$59.710$		$_{}$	None	None		$4$	$0$	$0$	$20$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1012.5.f.a	$1012$	$5$	1012.f	23.b	$2$	$80$	$80$	$104.610$		$_{}$	None	None		$2$	$0$	$0$	$10$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1012.5.h.a	$1012$	$5$	1012.h	11.b	$2$	$88$	$88$	$104.610$		$_{}$	None	None		$2$	$0$	$0$	$16$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1012.6.a.a	$1012$	$6$	1012.a	1.a	$1$	$23$	$23$	$162.308$		$_{}$	None	None	✓	$1$	$1$	$0$	$-18$	$-139$	$47$	$+$		$\mathrm{SU}(2)$
1012.6.a.b	$1012$	$6$	1012.a	1.a	$1$	$23$	$23$	$162.308$		$_{}$	None	None	✓	$1$	$1$	$0$	$18$	$-89$	$-461$	$+$		$\mathrm{SU}(2)$
1012.6.a.c	$1012$	$6$	1012.a	1.a	$1$	$24$	$24$	$162.308$		$_{}$	None	None	✓	$1$	$0$	$0$	$-18$	$111$	$-75$	$-$		$\mathrm{SU}(2)$
1012.6.a.d	$1012$	$6$	1012.a	1.a	$1$	$24$	$24$	$162.308$		$_{}$	None	None	✓	$1$	$0$	$0$	$18$	$161$	$53$	$-$		$\mathrm{SU}(2)$

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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.