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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 98 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
690.2.a.a	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
690.2.a.b	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
690.2.a.c	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
690.2.a.d	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
690.2.a.e	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
690.2.a.f	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
690.2.a.g	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
690.2.a.h	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
690.2.a.i	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
690.2.a.j	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
690.2.a.k	$690$	$2$	690.a	1.a	$1$	$1$	$1$	$5.510$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
690.2.a.l	$690$	$2$	690.a	1.a	$1$	$2$	$2$	$5.510$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$-2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
690.2.d.a	$690$	$2$	690.d	5.b	$2$	$4$	$4$	$5.510$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}+q^{6}+\cdots$
690.2.d.b	$690$	$2$	690.d	5.b	$2$	$4$	$4$	$5.510$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
690.2.d.c	$690$	$2$	690.d	5.b	$2$	$6$	$6$	$5.510$	6.0.350464.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots$
690.2.d.d	$690$	$2$	690.d	5.b	$2$	$6$	$6$	$5.510$	6.0.5161984.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}-q^{6}+\cdots$
690.2.e.a	$690$	$2$	690.e	69.c	$2$	$16$	$16$	$5.510$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$-16$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+\beta _{2}q^{3}-q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
690.2.e.b	$690$	$2$	690.e	69.c	$2$	$16$	$16$	$5.510$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$16$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}+\beta _{2}q^{3}-q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
690.2.h.a	$690$	$2$	690.h	345.h	$2$	$24$	$24$	$5.510$		None		$4$	$0$	$-24$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
690.2.h.b	$690$	$2$	690.h	345.h	$2$	$24$	$24$	$5.510$		None		$4$	$0$	$24$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
690.2.i.a	$690$	$2$	690.i	15.e	$4$	$4$	$2$	$5.510$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
690.2.i.b	$690$	$2$	690.i	15.e	$4$	$4$	$2$	$5.510$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
690.2.i.c	$690$	$2$	690.i	15.e	$4$	$8$	$4$	$5.510$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$-8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{24}^{5}q^{2}+(-1+\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots$
690.2.i.d	$690$	$2$	690.i	15.e	$4$	$8$	$4$	$5.510$	8.0.40960000.1	None		$4$	$0$	$0$	$-8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3})q^{3}-\beta _{3}q^{4}+\cdots$
690.2.i.e	$690$	$2$	690.i	15.e	$4$	$32$	$16$	$5.510$		None		$4$	$0$	$0$	$4$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
690.2.i.f	$690$	$2$	690.i	15.e	$4$	$32$	$16$	$5.510$		None		$4$	$0$	$0$	$4$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
690.2.j.a	$690$	$2$	690.j	115.e	$4$	$24$	$12$	$5.510$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
690.2.j.b	$690$	$2$	690.j	115.e	$4$	$24$	$12$	$5.510$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
690.2.m.a	$690$	$2$	690.m	23.c	$11$	$10$	$1$	$5.510$	$\Q(\zeta_{22})$	None		$2$	$0$	$-1$	$-1$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots$
690.2.m.b	$690$	$2$	690.m	23.c	$11$	$10$	$1$	$5.510$	$\Q(\zeta_{22})$	None		$2$	$0$	$1$	$-1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q-\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots$
690.2.m.c	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-2$	$2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{16}q^{2}-\beta _{14}q^{3}-\beta _{12}q^{4}+\beta _{11}q^{5}+\cdots$
690.2.m.d	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-2$	$2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{7}q^{2}-\beta _{12}q^{3}+\beta _{10}q^{4}-\beta _{6}q^{5}+\cdots$
690.2.m.e	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$2$	$2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q-\beta _{13}q^{2}-\beta _{16}q^{3}-\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
690.2.m.f	$690$	$2$	690.m	23.c	$11$	$20$	$2$	$5.510$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$2$	$2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{8}q^{2}+(1+\beta _{5}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots$
690.2.m.g	$690$	$2$	690.m	23.c	$11$	$30$	$3$	$5.510$		None		$2$	$0$	$-3$	$-3$	$-3$	$-8$			$\mathrm{SU}(2)[C_{11}]$
690.2.m.h	$690$	$2$	690.m	23.c	$11$	$30$	$3$	$5.510$		None		$2$	$0$	$3$	$-3$	$3$	$8$			$\mathrm{SU}(2)[C_{11}]$
690.2.n.a	$690$	$2$	690.n	345.n	$22$	$240$	$24$	$5.510$		None		$4$	$0$	$-24$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
690.2.n.b	$690$	$2$	690.n	345.n	$22$	$240$	$24$	$5.510$		None		$4$	$0$	$24$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
690.2.q.a	$690$	$2$	690.q	69.g	$22$	$160$	$16$	$5.510$		None		$2$	$0$	$0$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{22}]$
690.2.q.b	$690$	$2$	690.q	69.g	$22$	$160$	$16$	$5.510$		None		$2$	$0$	$0$	$0$	$16$	$0$			$\mathrm{SU}(2)[C_{22}]$
690.2.r.a	$690$	$2$	690.r	115.j	$22$	$120$	$12$	$5.510$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
690.2.r.b	$690$	$2$	690.r	115.j	$22$	$120$	$12$	$5.510$		None		$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{22}]$
690.2.w.a	$690$	$2$	690.w	115.l	$44$	$240$	$12$	$5.510$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
690.2.w.b	$690$	$2$	690.w	115.l	$44$	$240$	$12$	$5.510$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
690.2.x.a	$690$	$2$	690.x	345.x	$44$	$960$	$48$	$5.510$		None		$8$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
690.3.b.a	$690$	$3$	690.b	15.d	$2$	$88$	$88$	$18.801$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
690.3.c.a	$690$	$3$	690.c	23.b	$2$	$32$	$32$	$18.801$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
690.3.f.a	$690$	$3$	690.f	115.c	$2$	$48$	$48$	$18.801$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
690.3.g.a	$690$	$3$	690.g	3.b	$2$	$56$	$56$	$18.801$		None		$2$	$0$	$0$	$-8$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
690.3.k.a	$690$	$3$	690.k	5.c	$4$	$40$	$20$	$18.801$		None		$2$	$0$	$40$	$0$	$-8$	$-8$			$\mathrm{SU}(2)[C_{4}]$

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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.