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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 (30 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
361.2.e.d	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+2\zeta_{18}q^{3}+2\zeta_{18}^{5}q^{4}+3\zeta_{18}^{4}q^{5}+\cdots$
361.2.e.e	$361$	$2$	361.e	19.e	$9$	$6$	$1$	$2.883$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-2\zeta_{18}q^{3}+2\zeta_{18}^{5}q^{4}+3\zeta_{18}^{4}q^{5}+\cdots$
361.2.e.i	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$-18$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{7}q^{2}+(-\beta _{1}-2\beta _{3})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{4}+\cdots$
361.2.e.j	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$-18$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{7}-2\beta _{9})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots$
361.2.e.k	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{5}-2\beta _{10}+\beta _{11})q^{2}+2\beta _{5}q^{3}+\cdots$
361.2.e.l	$361$	$2$	361.e	19.e	$9$	$12$	$2$	$2.883$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\beta _{5}-2\beta _{10}+\beta _{11})q^{2}-2\beta _{5}q^{3}+\cdots$
722.2.e.c	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$-9$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.d	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$-9$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.e	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.f	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.g	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$9$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.h	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$9$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.i	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$12$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.j	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$12$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.n	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.3	None		$6$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
722.2.e.o	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.3	None		$6$	$0$	$0$	$0$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
722.2.e.p	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{9}q^{2}-2\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
722.2.e.q	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{3}-\beta _{9})q^{2}-2\beta _{1}q^{3}+(-\beta _{5}+\beta _{11})q^{4}+\cdots$
722.2.e.r	$722$	$2$	722.e	19.e	$9$	$24$	$4$	$5.765$		None		$6$	$0$	$0$	$0$	$0$	$6$		$\mathrm{SU}(2)[C_{9}]$
722.2.e.s	$722$	$2$	722.e	19.e	$9$	$24$	$4$	$5.765$		None		$6$	$0$	$0$	$0$	$0$	$6$		$\mathrm{SU}(2)[C_{9}]$
841.2.d.f	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.2	None		$6$	$0$	$-2$	$2$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\beta _{1}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
841.2.d.g	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$6$	$0$	$-1$	$1$	$-1$	$0$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
841.2.d.i	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.1	None		$6$	$0$	$1$	$-1$	$-1$	$0$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(\beta _{4}-\beta _{5})q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
841.2.d.j	$841$	$2$	841.d	29.d	$7$	$12$	$2$	$6.715$	12.0.$\cdots$.2	None		$6$	$0$	$2$	$-2$	$2$	$0$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\beta _{2}+\beta _{9})q^{2}+(-\beta _{3}+\beta _{10})q^{3}+\cdots$
841.2.d.n	$841$	$2$	841.d	29.d	$7$	$36$	$6$	$6.715$		None		$6$	$0$	$-2$	$-2$	$2$	$4$		$\mathrm{SU}(2)[C_{7}]$
841.2.d.o	$841$	$2$	841.d	29.d	$7$	$36$	$6$	$6.715$		None		$6$	$0$	$2$	$2$	$2$	$4$		$\mathrm{SU}(2)[C_{7}]$
841.2.d.p	$841$	$2$	841.d	29.d	$7$	$48$	$8$	$6.715$		None		$6$	$0$	$-4$	$-6$	$1$	$0$		$\mathrm{SU}(2)[C_{7}]$
841.2.d.q	$841$	$2$	841.d	29.d	$7$	$48$	$8$	$6.715$		None		$6$	$0$	$4$	$6$	$1$	$0$		$\mathrm{SU}(2)[C_{7}]$
361.3.f.h	$361$	$3$	361.f	19.f	$18$	$18$	$3$	$9.837$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$6$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(-\beta _{5}+\beta _{17})q^{2}+(-\beta _{4}-2\beta _{5}-2\beta _{11}+\cdots)q^{3}+\cdots$
361.3.f.i	$361$	$3$	361.f	19.f	$18$	$18$	$3$	$9.837$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$6$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(\beta _{5}-\beta _{17})q^{2}+(\beta _{4}+2\beta _{5}+2\beta _{11}+\cdots)q^{3}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.