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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 98 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
760.1.b.a	$760$	$1$	760.b	760.b	$2$	$8$	$8$	$0.379$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$
760.1.bm.a	$760$	$1$	760.bm	760.am	$6$	$2$	$1$	$0.379$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-2$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots$
760.1.bm.b	$760$	$1$	760.bm	760.am	$6$	$2$	$1$	$0.379$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$2$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}-q^{8}+\cdots$
760.1.bt.a	$760$	$1$	760.bt	95.m	$12$	$4$	$1$	$0.379$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots$
760.1.bz.a	$760$	$1$	760.bz	760.az	$18$	$6$	$1$	$0.379$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
760.1.bz.b	$760$	$1$	760.bz	760.az	$18$	$6$	$1$	$0.379$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{5}q^{5}+\cdots$
760.2.a.a	$760$	$2$	760.a	1.a	$1$	$1$	$1$	$6.069$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots$
760.2.a.b	$760$	$2$	760.a	1.a	$1$	$1$	$1$	$6.069$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$
760.2.a.c	$760$	$2$	760.a	1.a	$1$	$1$	$1$	$6.069$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-4q^{11}-6q^{13}-6q^{17}+\cdots$
760.2.a.d	$760$	$2$	760.a	1.a	$1$	$1$	$1$	$6.069$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
760.2.a.e	$760$	$2$	760.a	1.a	$1$	$1$	$1$	$6.069$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-q^{7}+6q^{9}+4q^{11}+\cdots$
760.2.a.f	$760$	$2$	760.a	1.a	$1$	$2$	$2$	$6.069$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+(2+2\beta )q^{11}+\cdots$
760.2.a.g	$760$	$2$	760.a	1.a	$1$	$2$	$2$	$6.069$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(1+2\beta )q^{9}+2q^{11}+\cdots$
760.2.a.h	$760$	$2$	760.a	1.a	$1$	$3$	$3$	$6.069$	3.3.568.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots$
760.2.a.i	$760$	$2$	760.a	1.a	$1$	$3$	$3$	$6.069$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots$
760.2.a.j	$760$	$2$	760.a	1.a	$1$	$3$	$3$	$6.069$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots$
760.2.d.a	$760$	$2$	760.d	5.b	$2$	$2$	$2$	$6.069$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots$
760.2.d.b	$760$	$2$	760.d	5.b	$2$	$4$	$4$	$6.069$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
760.2.d.c	$760$	$2$	760.d	5.b	$2$	$4$	$4$	$6.069$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots$
760.2.d.d	$760$	$2$	760.d	5.b	$2$	$4$	$4$	$6.069$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
760.2.d.e	$760$	$2$	760.d	5.b	$2$	$12$	$12$	$6.069$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{3}-\beta _{1}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots$
760.2.e.a	$760$	$2$	760.e	152.b	$2$	$80$	$80$	$6.069$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
760.2.f.a	$760$	$2$	760.f	8.b	$2$	$28$	$28$	$6.069$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
760.2.f.b	$760$	$2$	760.f	8.b	$2$	$44$	$44$	$6.069$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
760.2.k.a	$760$	$2$	760.k	40.f	$2$	$108$	$108$	$6.069$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
760.2.p.a	$760$	$2$	760.p	760.p	$2$	$4$	$4$	$6.069$	$\Q(\sqrt{-2}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{5}+2\beta _{3}q^{7}+\cdots$
760.2.p.b	$760$	$2$	760.p	760.p	$2$	$4$	$4$	$6.069$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots$
760.2.p.c	$760$	$2$	760.p	760.p	$2$	$4$	$4$	$6.069$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots$
760.2.p.d	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.1499238400.2	$_{}$	None	None		$4$	$0$	$-8$	$-8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{5})q^{2}-q^{3}+2\beta _{5}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots$
760.2.p.e	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.5473632256.3	$_{}$	None	None		$4$	$0$	$-4$	$8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$
760.2.p.f	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.5473632256.3	$_{}$	None	None		$4$	$0$	$4$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$
760.2.p.g	$760$	$2$	760.p	760.p	$2$	$8$	$8$	$6.069$	8.0.1499238400.2	$_{}$	None	None		$4$	$0$	$8$	$8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{5})q^{2}+q^{3}+2\beta _{5}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
760.2.p.h	$760$	$2$	760.p	760.p	$2$	$16$	$16$	$6.069$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}+\cdots$
760.2.p.i	$760$	$2$	760.p	760.p	$2$	$56$	$56$	$6.069$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
760.2.q.a	$760$	$2$	760.q	19.c	$3$	$2$	$1$	$6.069$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots$
760.2.q.b	$760$	$2$	760.q	19.c	$3$	$2$	$1$	$6.069$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-1$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+4q^{7}+\cdots$
760.2.q.c	$760$	$2$	760.q	19.c	$3$	$2$	$1$	$6.069$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$
760.2.q.d	$760$	$2$	760.q	19.c	$3$	$8$	$4$	$6.069$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots$
760.2.q.e	$760$	$2$	760.q	19.c	$3$	$8$	$4$	$6.069$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(1-\beta _{5})q^{5}+(-1-\beta _{4}+2\beta _{7})q^{7}+\cdots$
760.2.q.f	$760$	$2$	760.q	19.c	$3$	$8$	$4$	$6.069$	8.0.4601315889.1	$_{}$	None	None		$2$	$0$	$0$	$1$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{7}q^{3}-\beta _{5}q^{5}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
760.2.q.g	$760$	$2$	760.q	19.c	$3$	$10$	$5$	$6.069$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$1$	$5$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(1+\beta _{5})q^{7}+\cdots$
760.2.t.a	$760$	$2$	760.t	760.t	$4$	$232$	$116$	$6.069$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
760.2.v.a	$760$	$2$	760.v	95.g	$4$	$12$	$6$	$6.069$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$-12$	$-4$		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{10}q^{3}+(-1-2\beta _{5})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$
760.2.v.b	$760$	$2$	760.v	95.g	$4$	$48$	$24$	$6.069$		$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$4$			$\mathrm{SU}(2)[C_{4}]$
760.2.w.a	$760$	$2$	760.w	40.k	$4$	$2$	$1$	$6.069$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$4$	$2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}+(2-2i)q^{3}-2iq^{4}+\cdots$
760.2.w.b	$760$	$2$	760.w	40.k	$4$	$2$	$1$	$6.069$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$4$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{2}+(2-2i)q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots$
760.2.w.c	$760$	$2$	760.w	40.k	$4$	$104$	$52$	$6.069$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
760.2.w.d	$760$	$2$	760.w	40.k	$4$	$108$	$54$	$6.069$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
760.2.z.a	$760$	$2$	760.z	760.z	$6$	$232$	$116$	$6.069$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
760.2.bf.a	$760$	$2$	760.bf	760.af	$6$	$8$	$4$	$6.069$	8.0.207360000.2	$_{}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{1}q^{2}+(2+2\beta _{4})q^{4}-\beta _{6}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$

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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.