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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 (1-50 of 163 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
510.2.a.a	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
510.2.a.b	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
510.2.a.c	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
510.2.a.d	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
510.2.a.e	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
510.2.a.f	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
510.2.a.g	$510$	$2$	510.a	1.a	$1$	$1$	$1$	$4.072$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots$
510.2.a.h	$510$	$2$	510.a	1.a	$1$	$2$	$2$	$4.072$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$-2$	$-2$	$2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots$
510.2.c.a	$510$	$2$	510.c	17.b	$2$	$2$	$2$	$4.072$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}-iq^{5}-iq^{6}-q^{8}+\cdots$
510.2.c.b	$510$	$2$	510.c	17.b	$2$	$2$	$2$	$4.072$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots$
510.2.c.c	$510$	$2$	510.c	17.b	$2$	$4$	$4$	$4.072$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots$
510.2.c.d	$510$	$2$	510.c	17.b	$2$	$4$	$4$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\zeta_{8}q^{3}+q^{4}-\zeta_{8}q^{5}+\zeta_{8}q^{6}+\cdots$
510.2.d.a	$510$	$2$	510.d	5.b	$2$	$2$	$2$	$4.072$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}+(-2+i)q^{5}+\cdots$
510.2.d.b	$510$	$2$	510.d	5.b	$2$	$4$	$4$	$4.072$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}-q^{6}+\cdots$
510.2.d.c	$510$	$2$	510.d	5.b	$2$	$4$	$4$	$4.072$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
510.2.d.d	$510$	$2$	510.d	5.b	$2$	$6$	$6$	$4.072$	6.0.5161984.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{5}q^{5}+q^{6}+\cdots$
510.2.f.a	$510$	$2$	510.f	85.c	$2$	$4$	$4$	$4.072$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$-4$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{3}-q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots$
510.2.f.b	$510$	$2$	510.f	85.c	$2$	$4$	$4$	$4.072$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$4$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+q^{3}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots$
510.2.f.c	$510$	$2$	510.f	85.c	$2$	$6$	$6$	$4.072$	6.0.350464.1	None		$2$	$0$	$0$	$-6$	$-2$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
510.2.f.d	$510$	$2$	510.f	85.c	$2$	$6$	$6$	$4.072$	6.0.350464.1	None		$2$	$0$	$0$	$6$	$2$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots$
510.2.i.a	$510$	$2$	510.i	255.k	$4$	$72$	$36$	$4.072$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
510.2.l.a	$510$	$2$	510.l	15.e	$4$	$4$	$2$	$4.072$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$4$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
510.2.l.b	$510$	$2$	510.l	15.e	$4$	$4$	$2$	$4.072$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
510.2.l.c	$510$	$2$	510.l	15.e	$4$	$4$	$2$	$4.072$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
510.2.l.d	$510$	$2$	510.l	15.e	$4$	$8$	$4$	$4.072$	8.0.4030726144.1	None		$2$	$0$	$0$	$-8$	$4$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(-1-\beta _{4}+\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots$
510.2.l.e	$510$	$2$	510.l	15.e	$4$	$8$	$4$	$4.072$	8.0.4030726144.1	None		$2$	$0$	$0$	$0$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots$
510.2.l.f	$510$	$2$	510.l	15.e	$4$	$8$	$4$	$4.072$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{24}-\zeta_{24}^{5})q^{2}+(1-\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{3}+\cdots$
510.2.l.g	$510$	$2$	510.l	15.e	$4$	$28$	$14$	$4.072$		None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
510.2.m.a	$510$	$2$	510.m	85.j	$4$	$8$	$4$	$4.072$	8.0.110166016.2	None		$2$	$0$	$-8$	$0$	$-8$	$-4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+(-1+\beta _{3}-\beta _{7})q^{5}+\cdots$
510.2.m.b	$510$	$2$	510.m	85.j	$4$	$8$	$4$	$4.072$	8.0.110166016.2	None		$2$	$0$	$8$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots$
510.2.m.c	$510$	$2$	510.m	85.j	$4$	$12$	$6$	$4.072$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-12$	$0$	$4$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}-\beta _{7}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{7}q^{6}+\cdots$
510.2.m.d	$510$	$2$	510.m	85.j	$4$	$12$	$6$	$4.072$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$12$	$0$	$-4$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+\beta _{7}q^{3}+q^{4}+\beta _{5}q^{5}+\beta _{7}q^{6}+\cdots$
510.2.p.a	$510$	$2$	510.p	17.c	$4$	$4$	$2$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots$
510.2.p.b	$510$	$2$	510.p	17.c	$4$	$4$	$2$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{6}+\cdots$
510.2.p.c	$510$	$2$	510.p	17.c	$4$	$8$	$4$	$4.072$	8.0.18939904.2	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots$
510.2.p.d	$510$	$2$	510.p	17.c	$4$	$8$	$4$	$4.072$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{3}-q^{4}+\zeta_{16}^{4}q^{5}+\cdots$
510.2.q.a	$510$	$2$	510.q	255.o	$4$	$72$	$36$	$4.072$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
510.2.t.a	$510$	$2$	510.t	255.r	$4$	$72$	$36$	$4.072$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
510.2.u.a	$510$	$2$	510.u	17.d	$8$	$8$	$2$	$4.072$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$
510.2.u.b	$510$	$2$	510.u	17.d	$8$	$8$	$2$	$4.072$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{16}^{6}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{5}q^{5}+\cdots$
510.2.u.c	$510$	$2$	510.u	17.d	$8$	$16$	$4$	$4.072$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{5}q^{2}-\beta _{7}q^{3}+\beta _{1}q^{4}+\beta _{6}q^{5}+\cdots$
510.2.u.d	$510$	$2$	510.u	17.d	$8$	$16$	$4$	$4.072$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{6}$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{3}q^{2}-\beta _{9}q^{3}+\beta _{5}q^{4}-\beta _{1}q^{5}+\cdots$
510.2.w.a	$510$	$2$	510.w	255.aa	$8$	$4$	$1$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$0$	$-4$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+\cdots$
510.2.w.b	$510$	$2$	510.w	255.aa	$8$	$4$	$1$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$1$	$4$	$-4$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+q^{4}+\cdots$
510.2.w.c	$510$	$2$	510.w	255.aa	$8$	$68$	$17$	$4.072$		None		$2$	$0$	$-68$	$0$	$-8$	$8$			$\mathrm{SU}(2)[C_{8}]$
510.2.w.d	$510$	$2$	510.w	255.aa	$8$	$68$	$17$	$4.072$		None		$2$	$0$	$68$	$4$	$8$	$8$			$\mathrm{SU}(2)[C_{8}]$
510.2.z.a	$510$	$2$	510.z	255.v	$8$	$4$	$1$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{8}^{2}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
510.2.z.b	$510$	$2$	510.z	255.v	$8$	$4$	$1$	$4.072$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-\zeta_{8}^{2}q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
510.2.z.c	$510$	$2$	510.z	255.v	$8$	$68$	$17$	$4.072$		None		$2$	$0$	$0$	$-4$	$-8$	$-4$			$\mathrm{SU}(2)[C_{8}]$
510.2.z.d	$510$	$2$	510.z	255.v	$8$	$68$	$17$	$4.072$		None		$2$	$0$	$0$	$-4$	$8$	$-4$			$\mathrm{SU}(2)[C_{8}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.