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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 96 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
1450.2.a.a	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots$
1450.2.a.b	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots$
1450.2.a.c	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
1450.2.a.d	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-2q^{7}-q^{8}+\cdots$
1450.2.a.e	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+2q^{7}+q^{8}+\cdots$
1450.2.a.f	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}-4q^{13}+\cdots$
1450.2.a.g	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}+2q^{11}+\cdots$
1450.2.a.h	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
1450.2.a.i	$1450$	$2$	1450.a	1.a	$1$	$1$	$1$	$11.578$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+2q^{7}+q^{8}+\cdots$
1450.2.a.j	$1450$	$2$	1450.a	1.a	$1$	$2$	$2$	$11.578$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}+(-2-\beta )q^{7}+\cdots$
1450.2.a.k	$1450$	$2$	1450.a	1.a	$1$	$2$	$2$	$11.578$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$3$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
1450.2.a.l	$1450$	$2$	1450.a	1.a	$1$	$2$	$2$	$11.578$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-3$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots$
1450.2.a.m	$1450$	$2$	1450.a	1.a	$1$	$2$	$2$	$11.578$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-1$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(-3+\beta )q^{7}+\cdots$
1450.2.a.n	$1450$	$2$	1450.a	1.a	$1$	$2$	$2$	$11.578$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$2$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+(-1-\beta )q^{7}+\cdots$
1450.2.a.o	$1450$	$2$	1450.a	1.a	$1$	$2$	$2$	$11.578$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+(2-\beta )q^{7}+\cdots$
1450.2.a.p	$1450$	$2$	1450.a	1.a	$1$	$3$	$3$	$11.578$	3.3.621.1	None	✓	$1$	$1$	$-3$	$-3$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
1450.2.a.q	$1450$	$2$	1450.a	1.a	$1$	$3$	$3$	$11.578$	3.3.316.1	None	✓	$1$	$0$	$-3$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots$
1450.2.a.r	$1450$	$2$	1450.a	1.a	$1$	$3$	$3$	$11.578$	3.3.469.1	None	✓	$1$	$0$	$-3$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots$
1450.2.a.s	$1450$	$2$	1450.a	1.a	$1$	$3$	$3$	$11.578$	3.3.316.1	None	✓	$1$	$0$	$3$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
1450.2.a.t	$1450$	$2$	1450.a	1.a	$1$	$5$	$5$	$11.578$	5.5.3661564.1	None	✓	$1$	$1$	$-5$	$-3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
1450.2.a.u	$1450$	$2$	1450.a	1.a	$1$	$5$	$5$	$11.578$	5.5.3661564.1	None	✓	$1$	$0$	$5$	$3$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots$
1450.2.b.a	$1450$	$2$	1450.b	5.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+2iq^{7}+\cdots$
1450.2.b.b	$1450$	$2$	1450.b	5.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}-2iq^{7}+\cdots$
1450.2.b.c	$1450$	$2$	1450.b	5.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots$
1450.2.b.d	$1450$	$2$	1450.b	5.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}-2iq^{7}+iq^{8}+3q^{9}+\cdots$
1450.2.b.e	$1450$	$2$	1450.b	5.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots$
1450.2.b.f	$1450$	$2$	1450.b	5.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+3iq^{3}-q^{4}+3q^{6}-2iq^{7}+\cdots$
1450.2.b.g	$1450$	$2$	1450.b	5.b	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots$
1450.2.b.h	$1450$	$2$	1450.b	5.b	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots$
1450.2.b.i	$1450$	$2$	1450.b	5.b	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots$
1450.2.b.j	$1450$	$2$	1450.b	5.b	$2$	$6$	$6$	$11.578$	6.0.14077504.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots$
1450.2.b.k	$1450$	$2$	1450.b	5.b	$2$	$6$	$6$	$11.578$	6.0.399424.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1450.2.b.l	$1450$	$2$	1450.b	5.b	$2$	$6$	$6$	$11.578$	6.0.24681024.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots$
1450.2.c.a	$1450$	$2$	1450.c	29.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}+2q^{7}-iq^{8}+\cdots$
1450.2.c.b	$1450$	$2$	1450.c	29.b	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-4q^{7}-iq^{8}+3q^{9}+\cdots$
1450.2.c.c	$1450$	$2$	1450.c	29.b	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{29})$	None		$2$	$0$	$0$	$0$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots$
1450.2.c.d	$1450$	$2$	1450.c	29.b	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots$
1450.2.c.e	$1450$	$2$	1450.c	29.b	$2$	$10$	$10$	$11.578$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{5}q^{6}+\beta _{6}q^{7}+\cdots$
1450.2.c.f	$1450$	$2$	1450.c	29.b	$2$	$10$	$10$	$11.578$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{5}q^{6}-\beta _{6}q^{7}+\cdots$
1450.2.c.g	$1450$	$2$	1450.c	29.b	$2$	$16$	$16$	$11.578$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+(\beta _{7}-\beta _{8})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots$
1450.2.d.a	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$-2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+2iq^{7}-q^{8}-3q^{9}+iq^{11}+\cdots$
1450.2.d.b	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2iq^{7}-q^{8}+\cdots$
1450.2.d.c	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{3}+q^{4}-q^{6}+2iq^{7}+q^{8}+\cdots$
1450.2.d.d	$1450$	$2$	1450.d	145.d	$2$	$2$	$2$	$11.578$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+2iq^{7}+q^{8}-3q^{9}-iq^{11}+\cdots$
1450.2.d.e	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$-4$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots$
1450.2.d.f	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{29})$	None		$2$	$0$	$-4$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
1450.2.d.g	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{29})$	None		$2$	$0$	$4$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+(-1+\beta _{3})q^{6}+\cdots$
1450.2.d.h	$1450$	$2$	1450.d	145.d	$2$	$4$	$4$	$11.578$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$4$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(1-\beta _{2})q^{3}+q^{4}+(1-\beta _{2})q^{6}+\cdots$
1450.2.d.i	$1450$	$2$	1450.d	145.d	$2$	$10$	$10$	$11.578$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-10$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{5}q^{3}+q^{4}-\beta _{5}q^{6}+\beta _{2}q^{7}+\cdots$
1450.2.d.j	$1450$	$2$	1450.d	145.d	$2$	$10$	$10$	$11.578$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$10$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{5}q^{3}+q^{4}-\beta _{5}q^{6}+\beta _{2}q^{7}+\cdots$

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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.