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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 69 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
1122.2.a.a	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
1122.2.a.b	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots$
1122.2.a.c	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots$
1122.2.a.d	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
1122.2.a.e	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots$
1122.2.a.f	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots$
1122.2.a.g	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots$
1122.2.a.h	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots$
1122.2.a.i	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
1122.2.a.j	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
1122.2.a.k	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
1122.2.a.l	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots$
1122.2.a.m	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots$
1122.2.a.n	$1122$	$2$	1122.a	1.a	$1$	$1$	$1$	$8.959$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots$
1122.2.a.o	$1122$	$2$	1122.a	1.a	$1$	$2$	$2$	$8.959$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
1122.2.a.p	$1122$	$2$	1122.a	1.a	$1$	$2$	$2$	$8.959$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots$
1122.2.a.q	$1122$	$2$	1122.a	1.a	$1$	$2$	$2$	$8.959$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$2$	$0$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
1122.2.a.r	$1122$	$2$	1122.a	1.a	$1$	$2$	$2$	$8.959$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
1122.2.a.s	$1122$	$2$	1122.a	1.a	$1$	$3$	$3$	$8.959$	3.3.148.1	None	✓	$1$	$0$	$3$	$-3$	$0$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
1122.2.b.a	$1122$	$2$	1122.b	33.d	$2$	$16$	$16$	$8.959$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-16$	$1$	$0$	$0$		$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{9}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{9}q^{6}+\cdots$
1122.2.b.b	$1122$	$2$	1122.b	33.d	$2$	$16$	$16$	$8.959$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-16$	$1$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
1122.2.b.c	$1122$	$2$	1122.b	33.d	$2$	$16$	$16$	$8.959$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$16$	$1$	$0$	$0$		$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{9}q^{3}+q^{4}+\beta _{13}q^{5}-\beta _{9}q^{6}+\cdots$
1122.2.b.d	$1122$	$2$	1122.b	33.d	$2$	$16$	$16$	$8.959$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$16$	$1$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
1122.2.c.a	$1122$	$2$	1122.c	17.b	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots$
1122.2.c.b	$1122$	$2$	1122.c	17.b	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots$
1122.2.c.c	$1122$	$2$	1122.c	17.b	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-iq^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots$
1122.2.c.d	$1122$	$2$	1122.c	17.b	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-iq^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots$
1122.2.c.e	$1122$	$2$	1122.c	17.b	$2$	$4$	$4$	$8.959$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1122.2.c.f	$1122$	$2$	1122.c	17.b	$2$	$4$	$4$	$8.959$	$\Q(\zeta_{8})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots$
1122.2.c.g	$1122$	$2$	1122.c	17.b	$2$	$6$	$6$	$8.959$	6.0.419904.1	None		$2$	$0$	$6$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
1122.2.c.h	$1122$	$2$	1122.c	17.b	$2$	$10$	$10$	$8.959$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-10$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{7})q^{5}+\cdots$
1122.2.h.a	$1122$	$2$	1122.h	561.h	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$-2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1122.2.h.b	$1122$	$2$	1122.h	561.h	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
1122.2.h.c	$1122$	$2$	1122.h	561.h	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-2}) $	None		$2$	$1$	$2$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
1122.2.h.d	$1122$	$2$	1122.h	561.h	$2$	$2$	$2$	$8.959$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
1122.2.h.e	$1122$	$2$	1122.h	561.h	$2$	$4$	$4$	$8.959$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$4$	$0$	$-4$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-2\beta _{2}q^{7}+\cdots$
1122.2.h.f	$1122$	$2$	1122.h	561.h	$2$	$4$	$4$	$8.959$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$4$	$0$	$4$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-2\beta _{2}q^{7}+\cdots$
1122.2.h.g	$1122$	$2$	1122.h	561.h	$2$	$28$	$28$	$8.959$		None		$4$	$0$	$-28$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1122.2.h.h	$1122$	$2$	1122.h	561.h	$2$	$28$	$28$	$8.959$		None		$4$	$0$	$28$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1122.2.l.a	$1122$	$2$	1122.l	17.c	$4$	$4$	$2$	$8.959$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots$
1122.2.l.b	$1122$	$2$	1122.l	17.c	$4$	$4$	$2$	$8.959$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots$
1122.2.l.c	$1122$	$2$	1122.l	17.c	$4$	$4$	$2$	$8.959$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots$
1122.2.l.d	$1122$	$2$	1122.l	17.c	$4$	$4$	$2$	$8.959$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(2+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
1122.2.l.e	$1122$	$2$	1122.l	17.c	$4$	$12$	$6$	$8.959$	12.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$-12$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
1122.2.l.f	$1122$	$2$	1122.l	17.c	$4$	$16$	$8$	$8.959$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{10}q^{2}-\beta _{6}q^{3}-q^{4}+\beta _{15}q^{5}+\cdots$
1122.2.l.g	$1122$	$2$	1122.l	17.c	$4$	$20$	$10$	$8.959$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{8}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots$
1122.3.d.a	$1122$	$3$	1122.d	187.b	$2$	$72$	$72$	$30.572$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1122.3.f.a	$1122$	$3$	1122.f	11.b	$2$	$64$	$64$	$30.572$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1122.4.a.a	$1122$	$4$	1122.a	1.a	$1$	$1$	$1$	$66.200$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$-18$	$26$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots$
1122.4.a.b	$1122$	$4$	1122.a	1.a	$1$	$3$	$3$	$66.200$	3.3.2636.1	None	✓	$1$	$1$	$6$	$9$	$-20$	$-28$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-6+\beta _{1}+2\beta _{2})q^{5}+\cdots$

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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.