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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 (42 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
1500.1.l.a	$1500$	$1$	1500.l	60.l	$4$	$16$	$8$	$0.749$	$\Q(\zeta_{40})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{5}q^{2}-\zeta_{40}^{11}q^{3}+\zeta_{40}^{10}q^{4}+\cdots$
1500.1.l.b	$1500$	$1$	1500.l	60.l	$4$	$16$	$8$	$0.749$	$\Q(\zeta_{40})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{5}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
1500.2.a.a	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots$
1500.2.a.b	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{7}+q^{9}-4q^{11}+(2-4\beta )q^{13}+\cdots$
1500.2.a.c	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots$
1500.2.a.d	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(4-\beta )q^{7}+q^{9}+(3-4\beta )q^{11}+\cdots$
1500.2.a.e	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-3-\beta )q^{7}+q^{9}+(-1+4\beta )q^{11}+\cdots$
1500.2.a.f	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2\beta q^{7}+q^{9}-4q^{11}+(-2+\cdots)q^{13}+\cdots$
1500.2.a.g	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2\beta q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots$
1500.2.a.h	$1500$	$2$	1500.a	1.a	$1$	$2$	$2$	$11.978$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{7}+q^{9}+q^{11}+(1-2\beta )q^{13}+\cdots$
1500.2.d.a	$1500$	$2$	1500.d	5.b	$2$	$4$	$4$	$11.978$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+2\beta _{1}q^{7}-q^{9}-4q^{11}+(4\beta _{1}+\cdots)q^{13}+\cdots$
1500.2.d.b	$1500$	$2$	1500.d	5.b	$2$	$4$	$4$	$11.978$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+2\beta _{1}q^{7}-q^{9}+(2+2\beta _{2}+\cdots)q^{11}+\cdots$
1500.2.d.c	$1500$	$2$	1500.d	5.b	$2$	$4$	$4$	$11.978$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}+4\beta _{3})q^{7}-q^{9}+(3+4\beta _{2}+\cdots)q^{11}+\cdots$
1500.2.d.d	$1500$	$2$	1500.d	5.b	$2$	$4$	$4$	$11.978$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{7}-q^{9}+q^{11}+\cdots$
1500.2.i.a	$1500$	$2$	1500.i	15.e	$4$	$32$	$16$	$11.978$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1500.2.i.b	$1500$	$2$	1500.i	15.e	$4$	$32$	$16$	$11.978$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1500.2.m.a	$1500$	$2$	1500.m	25.d	$5$	$8$	$2$	$11.978$	8.0.26265625.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$-8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{6}+\beta _{7})q^{7}+\cdots$
1500.2.m.b	$1500$	$2$	1500.m	25.d	$5$	$8$	$2$	$11.978$	$\Q(\zeta_{15})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$8$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\zeta_{15}^{2}+\zeta_{15}^{4}+\zeta_{15}^{5})q^{3}+(\zeta_{15}+\cdots)q^{7}+\cdots$
1500.2.m.c	$1500$	$2$	1500.m	25.d	$5$	$24$	$6$	$11.978$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$16$			$\mathrm{SU}(2)[C_{5}]$
1500.2.m.d	$1500$	$2$	1500.m	25.d	$5$	$24$	$6$	$11.978$		$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$-16$			$\mathrm{SU}(2)[C_{5}]$
1500.2.o.a	$1500$	$2$	1500.o	25.e	$10$	$16$	$4$	$11.978$	$\Q(\zeta_{60})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{60}^{4}q^{3}+(-\zeta_{60}-\zeta_{60}^{2}+2\zeta_{60}^{4}+\cdots)q^{7}+\cdots$
1500.2.o.b	$1500$	$2$	1500.o	25.e	$10$	$16$	$4$	$11.978$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q-\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{6}+\beta _{10}+2\beta _{13}+\cdots)q^{7}+\cdots$
1500.2.o.c	$1500$	$2$	1500.o	25.e	$10$	$24$	$6$	$11.978$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
1500.3.b.a	$1500$	$3$	1500.b	15.d	$2$	$16$	$16$	$40.872$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-5$	$0$	$0$		$2^{6}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{13}q^{7}+(\beta _{3}+\beta _{4})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1500.3.b.b	$1500$	$3$	1500.b	15.d	$2$	$16$	$16$	$40.872$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$5$	$0$	$0$		$2^{6}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-\beta _{13}q^{7}+(-\beta _{3}-\beta _{7})q^{9}+\cdots$
1500.3.b.c	$1500$	$3$	1500.b	15.d	$2$	$32$	$32$	$40.872$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1500.3.g.a	$1500$	$3$	1500.g	3.b	$2$	$32$	$32$	$40.872$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1500.3.g.b	$1500$	$3$	1500.g	3.b	$2$	$32$	$32$	$40.872$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1500.3.k.a	$1500$	$3$	1500.k	5.c	$4$	$32$	$16$	$40.872$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1500.3.k.b	$1500$	$3$	1500.k	5.c	$4$	$32$	$16$	$40.872$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1500.4.a.a	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-18$	$0$	$-28$	$-$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-3q^{3}+(-4-\beta _{1}+\beta _{2})q^{7}+9q^{9}+\cdots$
1500.4.a.b	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-18$	$0$	$-23$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-3q^{3}+(-4+\beta _{1}+\beta _{2})q^{7}+9q^{9}+\cdots$
1500.4.a.c	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-18$	$0$	$7$	$-$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-3q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+9q^{9}+\cdots$
1500.4.a.d	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-18$	$0$	$12$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-3q^{3}+(1+\beta _{1}-\beta _{5})q^{7}+9q^{9}+(-6+\cdots)q^{11}+\cdots$
1500.4.a.e	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$18$	$0$	$-12$	$-$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1-\beta _{1}+\beta _{5})q^{7}+9q^{9}+\cdots$
1500.4.a.f	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$18$	$0$	$-7$	$-$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots$
1500.4.a.g	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$18$	$0$	$23$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+3q^{3}+(4-\beta _{1}-\beta _{2})q^{7}+9q^{9}+(10+\cdots)q^{11}+\cdots$
1500.4.a.h	$1500$	$4$	1500.a	1.a	$1$	$6$	$6$	$88.503$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$18$	$0$	$28$	$+$	$2^{2}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q+3q^{3}+(4+\beta _{1}-\beta _{2})q^{7}+9q^{9}+(-1+\cdots)q^{11}+\cdots$
1500.4.d.a	$1500$	$4$	1500.d	5.b	$2$	$12$	$12$	$88.503$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+(\beta _{8}-\beta _{10})q^{7}-9q^{9}+(-5+\cdots)q^{11}+\cdots$
1500.4.d.b	$1500$	$4$	1500.d	5.b	$2$	$12$	$12$	$88.503$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+3\beta _{1}q^{3}+(\beta _{1}+\beta _{2}-\beta _{5}-\beta _{8})q^{7}+\cdots$
1500.4.d.c	$1500$	$4$	1500.d	5.b	$2$	$12$	$12$	$88.503$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(2\beta _{2}-\beta _{6})q^{7}-9q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots$
1500.4.d.d	$1500$	$4$	1500.d	5.b	$2$	$12$	$12$	$88.503$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-3\beta _{6}q^{3}+(3\beta _{6}+\beta _{7}-\beta _{9})q^{7}-9q^{9}+\cdots$

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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.