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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 181 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
816.1.m.a	$816$	$1$	816.m	51.c	$2$	$1$	$1$	$0.407$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q-q^{3}-q^{5}+q^{9}+q^{11}-q^{13}+q^{15}+\cdots$
816.1.m.b	$816$	$1$	816.m	51.c	$2$	$1$	$1$	$0.407$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}+q^{9}-q^{11}-q^{13}+q^{15}+\cdots$
816.1.bc.a	$816$	$1$	816.bc	51.f	$4$	$4$	$2$	$0.407$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots$
816.2.a.a	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+4q^{7}+q^{9}-q^{11}-5q^{13}+\cdots$
816.2.a.b	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
816.2.a.c	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots$
816.2.a.d	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{13}-q^{17}+\cdots$
816.2.a.e	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-5q^{11}-5q^{13}+\cdots$
816.2.a.f	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
816.2.a.g	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+4q^{7}+q^{9}+3q^{11}+\cdots$
816.2.a.h	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots$
816.2.a.i	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots$
816.2.a.j	$816$	$2$	816.a	1.a	$1$	$1$	$1$	$6.516$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{9}+q^{11}+3q^{13}+\cdots$
816.2.a.k	$816$	$2$	816.a	1.a	$1$	$2$	$2$	$6.516$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}-4q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
816.2.a.l	$816$	$2$	816.a	1.a	$1$	$2$	$2$	$6.516$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(4+\cdots)q^{11}+\cdots$
816.2.a.m	$816$	$2$	816.a	1.a	$1$	$2$	$2$	$6.516$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots$
816.2.c.a	$816$	$2$	816.c	17.b	$2$	$2$	$2$	$6.516$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}-6q^{13}+\cdots$
816.2.c.b	$816$	$2$	816.c	17.b	$2$	$2$	$2$	$6.516$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+3iq^{5}-2iq^{7}-q^{9}+5iq^{11}+\cdots$
816.2.c.c	$816$	$2$	816.c	17.b	$2$	$2$	$2$	$6.516$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-4iq^{7}-q^{9}+4iq^{11}+2q^{13}+\cdots$
816.2.c.d	$816$	$2$	816.c	17.b	$2$	$2$	$2$	$6.516$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+iq^{5}-2iq^{7}-q^{9}-3iq^{11}+\cdots$
816.2.c.e	$816$	$2$	816.c	17.b	$2$	$4$	$4$	$6.516$	$\Q(i, \sqrt{33})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots$
816.2.c.f	$816$	$2$	816.c	17.b	$2$	$6$	$6$	$6.516$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$
816.2.e.a	$816$	$2$	816.e	12.b	$2$	$4$	$4$	$6.516$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{3}q^{3}+3\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots$
816.2.e.b	$816$	$2$	816.e	12.b	$2$	$8$	$8$	$6.516$	8.0.$\cdots$.8	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+2\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots$
816.2.e.c	$816$	$2$	816.e	12.b	$2$	$20$	$20$	$6.516$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{14}q^{3}-\beta _{15}q^{5}-\beta _{16}q^{7}+(\beta _{9}+\cdots)q^{9}+\cdots$
816.2.o.a	$816$	$2$	816.o	204.h	$2$	$4$	$4$	$6.516$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$0$	$-6$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
816.2.o.b	$816$	$2$	816.o	204.h	$2$	$4$	$4$	$6.516$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}-3q^{9}-3\beta _{1}q^{11}+\cdots$
816.2.o.c	$816$	$2$	816.o	204.h	$2$	$4$	$4$	$6.516$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$0$	$6$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+(1-\beta _{3})q^{5}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
816.2.o.d	$816$	$2$	816.o	204.h	$2$	$8$	$8$	$6.516$	8.0.$\cdots$.12	$_{}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{6})q^{7}-\beta _{2}q^{9}+\cdots$
816.2.o.e	$816$	$2$	816.o	204.h	$2$	$16$	$16$	$6.516$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}-\beta _{9}q^{5}+\beta _{10}q^{7}+(1+\beta _{7}+\cdots)q^{9}+\cdots$
816.2.r.a	$816$	$2$	816.r	816.r	$4$	$4$	$2$	$6.516$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-4$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots$
816.2.r.b	$816$	$2$	816.r	816.r	$4$	$4$	$2$	$6.516$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$4$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots$
816.2.r.c	$816$	$2$	816.r	816.r	$4$	$272$	$136$	$6.516$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
816.2.s.a	$816$	$2$	816.s	272.s	$4$	$2$	$1$	$6.516$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$
816.2.s.b	$816$	$2$	816.s	272.s	$4$	$2$	$1$	$6.516$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$
816.2.s.c	$816$	$2$	816.s	272.s	$4$	$68$	$34$	$6.516$		$_{}$	None	None		$2$	$0$	$-2$	$68$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
816.2.s.d	$816$	$2$	816.s	272.s	$4$	$72$	$36$	$6.516$		$_{}$	None	None		$2$	$0$	$-2$	$-72$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
816.2.u.a	$816$	$2$	816.u	16.e	$4$	$64$	$32$	$6.516$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
816.2.u.b	$816$	$2$	816.u	16.e	$4$	$64$	$32$	$6.516$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
816.2.w.a	$816$	$2$	816.w	816.w	$4$	$280$	$140$	$6.516$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
816.2.bd.a	$816$	$2$	816.bd	17.c	$4$	$4$	$2$	$6.516$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{3}+(-1+2\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
816.2.bd.b	$816$	$2$	816.bd	17.c	$4$	$4$	$2$	$6.516$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+\zeta_{8}q^{5}+(1-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots$
816.2.bd.c	$816$	$2$	816.bd	17.c	$4$	$4$	$2$	$6.516$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}q^{3}+(1+2\zeta_{8}+\zeta_{8}^{2})q^{5}-2\zeta_{8}^{3}q^{7}+\cdots$
816.2.bd.d	$816$	$2$	816.bd	17.c	$4$	$4$	$2$	$6.516$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+(2+\zeta_{8}+2\zeta_{8}^{2})q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
816.2.bd.e	$816$	$2$	816.bd	17.c	$4$	$8$	$4$	$6.516$	8.0.836829184.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+(-1+\beta _{3}+\beta _{4}+\beta _{7})q^{5}+\cdots$
816.2.bd.f	$816$	$2$	816.bd	17.c	$4$	$12$	$6$	$6.516$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{3}+\beta _{6}q^{5}+(\beta _{4}+\beta _{10})q^{7}-\beta _{5}q^{9}+\cdots$
816.2.bf.a	$816$	$2$	816.bf	204.l	$4$	$8$	$4$	$6.516$	8.0.12960000.1	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{2}+\beta _{5})q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+\cdots$
816.2.bf.b	$816$	$2$	816.bf	204.l	$4$	$8$	$4$	$6.516$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{24}^{7}q^{3}+\zeta_{24}q^{5}+(-\zeta_{24}^{4}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots$
816.2.bf.c	$816$	$2$	816.bf	204.l	$4$	$8$	$4$	$6.516$	8.0.12960000.1	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{1}+\beta _{5})q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}+\cdots$
816.2.bf.d	$816$	$2$	816.bf	204.l	$4$	$24$	$12$	$6.516$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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Elliptic curves over $\Q$
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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.