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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 83 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
1000.1.e.a	$1000$	$1$	1000.e	40.e	$2$	$2$	$2$	$0.499$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$1$		$1$		$q-q^{2}+q^{4}+(1-\beta )q^{7}-q^{8}+q^{9}+\cdots$
1000.1.e.b	$1000$	$1$	1000.e	40.e	$2$	$2$	$2$	$0.499$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+q^{9}+\cdots$
1000.1.g.a	$1000$	$1$	1000.g	8.d	$2$	$4$	$4$	$0.499$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{3}q^{2}-q^{4}-\beta _{1}q^{7}+\beta _{3}q^{8}-q^{9}+\cdots$
1000.2.a.a	$1000$	$2$	1000.a	1.a	$1$	$2$	$2$	$7.985$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
1000.2.a.b	$1000$	$2$	1000.a	1.a	$1$	$2$	$2$	$7.985$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
1000.2.a.c	$1000$	$2$	1000.a	1.a	$1$	$2$	$2$	$7.985$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
1000.2.a.d	$1000$	$2$	1000.a	1.a	$1$	$2$	$2$	$7.985$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots$
1000.2.a.e	$1000$	$2$	1000.a	1.a	$1$	$4$	$4$	$7.985$	4.4.4400.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{2}-\beta _{3})q^{7}+\cdots$
1000.2.a.f	$1000$	$2$	1000.a	1.a	$1$	$4$	$4$	$7.985$	4.4.10025.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots$
1000.2.a.g	$1000$	$2$	1000.a	1.a	$1$	$4$	$4$	$7.985$	4.4.10025.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(2+\beta _{3})q^{7}+(2-\beta _{2}+\beta _{3})q^{9}+\cdots$
1000.2.a.h	$1000$	$2$	1000.a	1.a	$1$	$4$	$4$	$7.985$	4.4.4400.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(2+\beta _{2}-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
1000.2.c.a	$1000$	$2$	1000.c	5.b	$2$	$4$	$4$	$7.985$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(2\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$
1000.2.c.b	$1000$	$2$	1000.c	5.b	$2$	$4$	$4$	$7.985$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$
1000.2.c.c	$1000$	$2$	1000.c	5.b	$2$	$8$	$8$	$7.985$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(3\beta _{2}+\beta _{3}-\beta _{7})q^{7}+(-3+\cdots)q^{9}+\cdots$
1000.2.c.d	$1000$	$2$	1000.c	5.b	$2$	$8$	$8$	$7.985$	8.0.309760000.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}+\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$
1000.2.d.a	$1000$	$2$	1000.d	8.b	$2$	$4$	$4$	$7.985$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{2}+2\beta _{1}q^{3}-2\beta _{3}q^{4}+\cdots$
1000.2.d.b	$1000$	$2$	1000.d	8.b	$2$	$4$	$4$	$7.985$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{3})q^{2}+2\beta _{1}q^{3}+2\beta _{3}q^{4}+(2\beta _{1}+\cdots)q^{6}+\cdots$
1000.2.d.c	$1000$	$2$	1000.d	8.b	$2$	$40$	$40$	$7.985$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1000.2.d.d	$1000$	$2$	1000.d	8.b	$2$	$48$	$48$	$7.985$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1000.2.f.a	$1000$	$2$	1000.f	40.f	$2$	$4$	$4$	$7.985$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-4$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{3})q^{2}+(-2-2\beta _{2})q^{3}+2\beta _{3}q^{4}+\cdots$
1000.2.f.b	$1000$	$2$	1000.f	40.f	$2$	$4$	$4$	$7.985$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$4$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{2}+(2+2\beta _{2})q^{3}-2\beta _{3}q^{4}+\cdots$
1000.2.f.c	$1000$	$2$	1000.f	40.f	$2$	$20$	$20$	$7.985$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{14}q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$
1000.2.f.d	$1000$	$2$	1000.f	40.f	$2$	$20$	$20$	$7.985$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$3$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{14}q^{3}+\beta _{2}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$
1000.2.f.e	$1000$	$2$	1000.f	40.f	$2$	$48$	$48$	$7.985$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1000.2.k.a	$1000$	$2$	1000.k	40.k	$4$	$8$	$4$	$7.985$	8.0.1024000000.2	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-8$	$0$	$0$	$4$		$5^{4}$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+\beta _{3}q^{7}+\cdots$
1000.2.k.b	$1000$	$2$	1000.k	40.k	$4$	$8$	$4$	$7.985$	8.0.1024000000.2	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$8$	$0$	$0$	$-4$		$5^{4}$	$\mathrm{U}(1)[D_{4}]$	$q+(1+\beta _{1})q^{2}+2\beta _{1}q^{4}-\beta _{3}q^{7}+(-2+\cdots)q^{8}+\cdots$
1000.2.k.c	$1000$	$2$	1000.k	40.k	$4$	$16$	$8$	$7.985$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$-4$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{7}+\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots$
1000.2.k.d	$1000$	$2$	1000.k	40.k	$4$	$16$	$8$	$7.985$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{15}q^{2}+(\beta _{1}+\beta _{14})q^{3}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
1000.2.k.e	$1000$	$2$	1000.k	40.k	$4$	$16$	$8$	$7.985$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$4$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(\beta _{3}+\beta _{7}-\beta _{12})q^{3}+(-1+\cdots)q^{4}+\cdots$
1000.2.k.f	$1000$	$2$	1000.k	40.k	$4$	$64$	$32$	$7.985$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1000.2.k.g	$1000$	$2$	1000.k	40.k	$4$	$64$	$32$	$7.985$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1000.2.m.a	$1000$	$2$	1000.m	25.d	$5$	$4$	$1$	$7.985$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-5$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+2\zeta_{10}+\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1000.2.m.b	$1000$	$2$	1000.m	25.d	$5$	$8$	$2$	$7.985$	8.0.58140625.2	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$-4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{2})q^{3}+(-\beta _{1}+\beta _{4}+\beta _{5})q^{7}+\cdots$
1000.2.m.c	$1000$	$2$	1000.m	25.d	$5$	$16$	$4$	$7.985$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$6$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{1}q^{3}-\beta _{10}q^{7}+(\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$
1000.2.m.d	$1000$	$2$	1000.m	25.d	$5$	$32$	$8$	$7.985$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$16$			$\mathrm{SU}(2)[C_{5}]$
1000.2.m.e	$1000$	$2$	1000.m	25.d	$5$	$32$	$8$	$7.985$		$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-16$			$\mathrm{SU}(2)[C_{5}]$
1000.2.o.a	$1000$	$2$	1000.o	200.o	$10$	$112$	$28$	$7.985$		$_{}$	None	None		$4$	$0$	$5$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1000.2.o.b	$1000$	$2$	1000.o	200.o	$10$	$224$	$56$	$7.985$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1000.2.q.a	$1000$	$2$	1000.q	25.e	$10$	$8$	$2$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\cdots$
1000.2.q.b	$1000$	$2$	1000.q	25.e	$10$	$16$	$4$	$7.985$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+(\beta _{9}+\beta _{10})q^{3}+(-\beta _{5}+\beta _{9}+\beta _{11}+\cdots)q^{7}+\cdots$
1000.2.q.c	$1000$	$2$	1000.q	25.e	$10$	$32$	$8$	$7.985$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1000.2.q.d	$1000$	$2$	1000.q	25.e	$10$	$32$	$8$	$7.985$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1000.2.t.a	$1000$	$2$	1000.t	200.t	$10$	$112$	$28$	$7.985$		$_{}$	None	None		$4$	$0$	$3$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{10}]$
1000.2.t.b	$1000$	$2$	1000.t	200.t	$10$	$224$	$56$	$7.985$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1000.2.v.a	$1000$	$2$	1000.v	200.v	$20$	$8$	$1$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$-8$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
1000.2.v.b	$1000$	$2$	1000.v	200.v	$20$	$8$	$1$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
1000.2.v.c	$1000$	$2$	1000.v	200.v	$20$	$8$	$1$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(\zeta_{20}+\zeta_{20}^{6})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
1000.2.v.d	$1000$	$2$	1000.v	200.v	$20$	$8$	$1$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(\zeta_{20}+\zeta_{20}^{6})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
1000.2.v.e	$1000$	$2$	1000.v	200.v	$20$	$8$	$1$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$8$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(1-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
1000.2.v.f	$1000$	$2$	1000.v	200.v	$20$	$8$	$1$	$7.985$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$8$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(1-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{3}+\cdots$

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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.