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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 (33 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
3750.2.a.a	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots$
3750.2.a.b	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
3750.2.a.c	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3\beta q^{7}-q^{8}+\cdots$
3750.2.a.d	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta )q^{7}+\cdots$
3750.2.a.e	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+3\beta q^{7}+q^{8}+\cdots$
3750.2.a.f	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots$
3750.2.a.g	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
3750.2.a.h	$3750$	$2$	3750.a	1.a	$1$	$2$	$2$	$29.944$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots$
3750.2.a.i	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$1$	$-4$	$-4$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.a.j	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$-4$	$-4$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(2+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
3750.2.a.k	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$1$	$-4$	$4$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.a.l	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	4.4.32625.1	None	✓	$1$	$0$	$-4$	$4$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-\beta _{1}q^{7}-q^{8}+\cdots$
3750.2.a.m	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{20})^+$	None	✓	$1$	$1$	$-4$	$4$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1-\beta _{1}+\beta _{3})q^{7}+\cdots$
3750.2.a.n	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$-4$	$4$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
3750.2.a.o	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{20})^+$	None	✓	$1$	$1$	$4$	$-4$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.a.p	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$1$	$4$	$-4$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.a.q	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	4.4.32625.1	None	✓	$1$	$0$	$4$	$-4$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+\beta _{1}q^{7}+q^{8}+\cdots$
3750.2.a.r	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$4$	$-4$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
3750.2.a.s	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$1$	$4$	$4$	$0$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.a.t	$3750$	$2$	3750.a	1.a	$1$	$4$	$4$	$29.944$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$4$	$4$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(2-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
3750.2.a.u	$3750$	$2$	3750.a	1.a	$1$	$8$	$8$	$29.944$	8.8.$\cdots$.1	None	✓	$1$	$0$	$-8$	$-8$	$0$	$-4$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta _{6}+\cdots)q^{7}+\cdots$
3750.2.a.v	$3750$	$2$	3750.a	1.a	$1$	$8$	$8$	$29.944$	8.8.$\cdots$.1	None	✓	$1$	$0$	$8$	$8$	$0$	$4$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(1-\beta _{6})q^{7}+\cdots$
3750.2.c.a	$3750$	$2$	3750.c	5.b	$2$	$4$	$4$	$29.944$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+3\beta _{1}q^{7}+\cdots$
3750.2.c.b	$3750$	$2$	3750.c	5.b	$2$	$4$	$4$	$29.944$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
3750.2.c.c	$3750$	$2$	3750.c	5.b	$2$	$4$	$4$	$29.944$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+q^{6}-2\beta _{3}q^{7}+\cdots$
3750.2.c.d	$3750$	$2$	3750.c	5.b	$2$	$4$	$4$	$29.944$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots$
3750.2.c.e	$3750$	$2$	3750.c	5.b	$2$	$8$	$8$	$29.944$	$\Q(\zeta_{20})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{20}q^{2}-\zeta_{20}q^{3}-q^{4}-q^{6}+(\zeta_{20}+\cdots)q^{7}+\cdots$
3750.2.c.f	$3750$	$2$	3750.c	5.b	$2$	$8$	$8$	$29.944$	8.0.324000000.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{5}q^{3}-q^{4}-q^{6}+(\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$
3750.2.c.g	$3750$	$2$	3750.c	5.b	$2$	$8$	$8$	$29.944$	8.0.324000000.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{5}q^{3}-q^{4}-q^{6}+(\beta _{1}+2\beta _{3}+\cdots)q^{7}+\cdots$
3750.2.c.h	$3750$	$2$	3750.c	5.b	$2$	$8$	$8$	$29.944$	8.0.$\cdots$.17	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}-q^{6}+\beta _{1}q^{7}+\cdots$
3750.2.c.i	$3750$	$2$	3750.c	5.b	$2$	$8$	$8$	$29.944$	8.0.324000000.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{5}q^{3}-q^{4}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.c.j	$3750$	$2$	3750.c	5.b	$2$	$8$	$8$	$29.944$	8.0.324000000.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{5}q^{3}-q^{4}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
3750.2.c.k	$3750$	$2$	3750.c	5.b	$2$	$16$	$16$	$29.944$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+\beta _{6}q^{3}-q^{4}+q^{6}+(-\beta _{6}+\cdots)q^{7}+\cdots$

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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.