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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 265 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
650.2.a.a	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
650.2.a.b	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots$
650.2.a.c	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+4q^{7}-q^{8}+\cdots$
650.2.a.d	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-q^{13}+q^{16}+\cdots$
650.2.a.e	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots$
650.2.a.f	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-5q^{7}-q^{8}+\cdots$
650.2.a.g	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{7}-q^{8}+\cdots$
650.2.a.h	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+5q^{7}+q^{8}+\cdots$
650.2.a.i	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
650.2.a.j	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
650.2.a.k	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots$
650.2.a.l	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+4q^{7}+q^{8}+\cdots$
650.2.a.m	$650$	$2$	650.a	1.a	$1$	$1$	$1$	$5.190$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
650.2.a.n	$650$	$2$	650.a	1.a	$1$	$3$	$3$	$5.190$	3.3.940.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
650.2.a.o	$650$	$2$	650.a	1.a	$1$	$3$	$3$	$5.190$	3.3.940.1	None	✓	$1$	$0$	$3$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
650.2.b.a	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+3iq^{3}-q^{4}-3q^{6}+iq^{7}+\cdots$
650.2.b.b	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+5iq^{7}+\cdots$
650.2.b.c	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}-4iq^{7}+\cdots$
650.2.b.d	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$
650.2.b.e	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-iq^{8}+3q^{9}-iq^{13}+\cdots$
650.2.b.f	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+4iq^{7}+\cdots$
650.2.b.g	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-4iq^{7}+\cdots$
650.2.b.h	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+iq^{7}+\cdots$
650.2.b.i	$650$	$2$	650.b	5.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-3iq^{3}-q^{4}+3q^{6}-iq^{8}+\cdots$
650.2.c.a	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}-iq^{6}-3q^{7}-q^{8}+\cdots$
650.2.c.b	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots$
650.2.c.c	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+iq^{6}+q^{8}-q^{9}+\cdots$
650.2.c.d	$650$	$2$	650.c	65.d	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+iq^{6}+3q^{7}+q^{8}+\cdots$
650.2.c.e	$650$	$2$	650.c	65.d	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	$-6$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots$
650.2.c.f	$650$	$2$	650.c	65.d	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	$6$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
650.2.d.a	$650$	$2$	650.d	13.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-2q^{3}-q^{4}+2iq^{6}+iq^{8}+\cdots$
650.2.d.b	$650$	$2$	650.d	13.b	$2$	$2$	$2$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}+iq^{6}+3iq^{7}+\cdots$
650.2.d.c	$650$	$2$	650.d	13.b	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{1}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
650.2.d.d	$650$	$2$	650.d	13.b	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{1}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
650.2.d.e	$650$	$2$	650.d	13.b	$2$	$8$	$8$	$5.190$	8.0.303595776.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{5}q^{3}-q^{4}-\beta _{1}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$
650.2.e.a	$650$	$2$	650.e	13.c	$3$	$2$	$1$	$5.190$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-2$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
650.2.e.b	$650$	$2$	650.e	13.c	$3$	$2$	$1$	$5.190$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{7}-q^{8}+\cdots$
650.2.e.c	$650$	$2$	650.e	13.c	$3$	$2$	$1$	$5.190$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{7}-q^{8}+\cdots$
650.2.e.d	$650$	$2$	650.e	13.c	$3$	$4$	$2$	$5.190$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$2$	$0$	$-2$	$-1$	$0$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
650.2.e.e	$650$	$2$	650.e	13.c	$3$	$4$	$2$	$5.190$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$-2$	$1$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\cdots$
650.2.e.f	$650$	$2$	650.e	13.c	$3$	$4$	$2$	$5.190$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$2$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
650.2.e.g	$650$	$2$	650.e	13.c	$3$	$4$	$2$	$5.190$	$\Q(\sqrt{-3}, \sqrt{13})$	None		$2$	$0$	$2$	$-1$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
650.2.e.h	$650$	$2$	650.e	13.c	$3$	$4$	$2$	$5.190$	$\Q(\sqrt{-3}, \sqrt{10})$	None		$2$	$0$	$2$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
650.2.e.i	$650$	$2$	650.e	13.c	$3$	$4$	$2$	$5.190$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$2$	$0$	$2$	$1$	$0$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
650.2.e.j	$650$	$2$	650.e	13.c	$3$	$6$	$3$	$5.190$	6.0.591408.1	None		$2$	$0$	$-3$	$0$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}-\beta _{5}q^{3}-\beta _{4}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots$
650.2.e.k	$650$	$2$	650.e	13.c	$3$	$6$	$3$	$5.190$	6.0.591408.1	None		$2$	$0$	$3$	$0$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(\beta _{3}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
650.2.g.a	$650$	$2$	650.g	65.k	$4$	$2$	$1$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+q^{4}+2iq^{7}-q^{8}-3iq^{9}+\cdots$
650.2.g.b	$650$	$2$	650.g	65.k	$4$	$2$	$1$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(1+i)q^{3}+q^{4}+(-1-i)q^{6}+\cdots$
650.2.g.c	$650$	$2$	650.g	65.k	$4$	$2$	$1$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-1-i)q^{3}+q^{4}+(-1-i)q^{6}+\cdots$
650.2.g.d	$650$	$2$	650.g	65.k	$4$	$2$	$1$	$5.190$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+q^{4}-2iq^{7}+q^{8}-3iq^{9}+\cdots$

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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.