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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 301 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
800.1.e.a	$800$	$1$	800.e	40.e	$2$	$2$	$2$	$0.399$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+q^{11}-iq^{17}-q^{19}-iq^{27}+\cdots$
800.1.g.a	$800$	$1$	800.g	8.d	$2$	$1$	$1$	$0.399$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{11}+q^{17}+q^{19}+q^{27}+\cdots$
800.1.g.b	$800$	$1$	800.g	8.d	$2$	$1$	$1$	$0.399$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{11}-q^{17}+q^{19}-q^{27}+\cdots$
800.1.p.a	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q+(-1+i)q^{3}+(1+i)q^{7}-iq^{9}-q^{21}+\cdots$
800.1.p.b	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{9}+(1-i)q^{13}+(1+i)q^{17}+(-1+\cdots)q^{37}+\cdots$
800.1.p.c	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+(1-i)q^{3}+(-1-i)q^{7}-iq^{9}-q^{21}+\cdots$
800.1.bh.a	$800$	$1$	800.bh	100.j	$10$	$8$	$2$	$0.399$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{5}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots$
800.1.bo.a	$800$	$1$	800.bo	25.f	$20$	$8$	$1$	$0.399$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{7}q^{5}+\zeta_{20}q^{9}+(-\zeta_{20}^{8}+\zeta_{20}^{9}+\cdots)q^{13}+\cdots$
800.2.a.a	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
800.2.a.b	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-5q^{11}+5q^{17}+\cdots$
800.2.a.c	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}+5q^{11}-5q^{17}+\cdots$
800.2.a.d	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-6q^{13}-2q^{17}-10q^{29}+\cdots$
800.2.a.e	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-4q^{13}-8q^{17}+10q^{29}+\cdots$
800.2.a.f	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+4q^{13}+8q^{17}+10q^{29}+\cdots$
800.2.a.g	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-5q^{11}-5q^{17}+\cdots$
800.2.a.h	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+5q^{11}+5q^{17}+\cdots$
800.2.a.i	$800$	$2$	800.a	1.a	$1$	$1$	$1$	$6.388$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
800.2.a.j	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$-6$	$+$	$2$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{3}+(-3+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
800.2.a.k	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{7}+2q^{9}+\beta q^{11}-4q^{13}+\cdots$
800.2.a.l	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{7}+2q^{9}-\beta q^{11}+4q^{13}+\cdots$
800.2.a.m	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+5q^{9}+2\beta q^{11}+2q^{13}+\cdots$
800.2.a.n	$800$	$2$	800.a	1.a	$1$	$2$	$2$	$6.388$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$6$	$-$	$2$	$N(\mathrm{U}(1))$	$q+(1+\beta )q^{3}+(3-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
800.2.c.a	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots$
800.2.c.b	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots$
800.2.c.c	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{7}+2q^{9}-5q^{11}+5iq^{17}+\cdots$
800.2.c.d	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{7}+2q^{9}+5q^{11}-5iq^{17}+\cdots$
800.2.c.e	$800$	$2$	800.c	5.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{9}+3iq^{13}-iq^{17}+10q^{29}+\cdots$
800.2.c.f	$800$	$2$	800.c	5.b	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{7}-5q^{9}+\zeta_{8}^{3}q^{11}+\cdots$
800.2.c.g	$800$	$2$	800.c	5.b	$2$	$4$	$4$	$6.388$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-2\beta _{2}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots$
800.2.d.a	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$-8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-4q^{7}-4q^{9}+\beta q^{11}-3q^{17}+\cdots$
800.2.d.b	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}-2q^{7}+2q^{9}-5iq^{11}-6iq^{13}+\cdots$
800.2.d.c	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2q^{7}+2q^{9}+5iq^{11}-6iq^{13}+\cdots$
800.2.d.d	$800$	$2$	800.d	8.b	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+4q^{7}-4q^{9}-\beta q^{11}+3q^{17}+\cdots$
800.2.d.e	$800$	$2$	800.d	8.b	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}^{3}q^{3}+(-1-\zeta_{12})q^{7}+(-1+\cdots)q^{9}+\cdots$
800.2.d.f	$800$	$2$	800.d	8.b	$2$	$4$	$4$	$6.388$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{7}+q^{9}+\beta _{3}q^{11}-2\beta _{2}q^{17}+\cdots$
800.2.f.a	$800$	$2$	800.f	40.f	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-2iq^{7}-2q^{9}+5iq^{11}+6q^{13}+\cdots$
800.2.f.b	$800$	$2$	800.f	40.f	$2$	$2$	$2$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2iq^{7}-2q^{9}+5iq^{11}-6q^{13}+\cdots$
800.2.f.c	$800$	$2$	800.f	40.f	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\zeta_{12})q^{3}+\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots$
800.2.f.d	$800$	$2$	800.f	40.f	$2$	$4$	$4$	$6.388$	$\Q(i, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+4\beta _{1}q^{7}+4q^{9}-\beta _{3}q^{11}+\cdots$
800.2.f.e	$800$	$2$	800.f	40.f	$2$	$4$	$4$	$6.388$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{12})q^{3}-\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots$
800.2.n.a	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2i)q^{3}+(-2+2i)q^{7}+5iq^{9}+\cdots$
800.2.n.b	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(-1+i)q^{7}-iq^{9}+\cdots$
800.2.n.c	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(-1+i)q^{7}-iq^{9}+\cdots$
800.2.n.d	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(-1+i)q^{7}-iq^{9}+\cdots$
800.2.n.e	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(3-3i)q^{7}-iq^{9}+\cdots$
800.2.n.f	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(-3+3i)q^{7}-iq^{9}+\cdots$
800.2.n.g	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(1-i)q^{7}-iq^{9}+4iq^{11}+\cdots$
800.2.n.h	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(1-i)q^{7}-iq^{9}-6iq^{11}+\cdots$
800.2.n.i	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(1-i)q^{7}-iq^{9}-4iq^{11}+\cdots$
800.2.n.j	$800$	$2$	800.n	20.e	$4$	$2$	$1$	$6.388$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2i)q^{3}+(2-2i)q^{7}+5iq^{9}+\cdots$

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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.