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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 153 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
462.2.a.a	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
462.2.a.b	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
462.2.a.c	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
462.2.a.d	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
462.2.a.e	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{7}+\cdots$
462.2.a.f	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
462.2.a.g	$462$	$2$	462.a	1.a	$1$	$1$	$1$	$3.689$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
462.2.a.h	$462$	$2$	462.a	1.a	$1$	$2$	$2$	$3.689$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots$
462.2.c.a	$462$	$2$	462.c	33.d	$2$	$12$	$12$	$3.689$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-12$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}-\beta _{6}q^{6}+\cdots$
462.2.c.b	$462$	$2$	462.c	33.d	$2$	$12$	$12$	$3.689$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$12$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}+\beta _{6}q^{6}+\cdots$
462.2.e.a	$462$	$2$	462.e	77.b	$2$	$8$	$8$	$3.689$	8.0.6679465984.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
462.2.e.b	$462$	$2$	462.e	77.b	$2$	$8$	$8$	$3.689$	8.0.6679465984.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
462.2.g.a	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$-2$	$-4$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots$
462.2.g.b	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	$\Q(i, \sqrt{6})$	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
462.2.g.c	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots$
462.2.g.d	$462$	$2$	462.g	21.c	$2$	$4$	$4$	$3.689$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$2$	$4$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
462.2.g.e	$462$	$2$	462.g	21.c	$2$	$8$	$8$	$3.689$	8.0.342102016.5	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots$
462.2.i.a	$462$	$2$	462.i	7.c	$3$	$2$	$1$	$3.689$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
462.2.i.b	$462$	$2$	462.i	7.c	$3$	$2$	$1$	$3.689$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
462.2.i.c	$462$	$2$	462.i	7.c	$3$	$2$	$1$	$3.689$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
462.2.i.d	$462$	$2$	462.i	7.c	$3$	$2$	$1$	$3.689$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
462.2.i.e	$462$	$2$	462.i	7.c	$3$	$4$	$2$	$3.689$	$\Q(\sqrt{-3}, \sqrt{7})$	None		$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$
462.2.i.f	$462$	$2$	462.i	7.c	$3$	$6$	$3$	$3.689$	6.0.1156923.1	None		$2$	$0$	$-3$	$-3$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
462.2.i.g	$462$	$2$	462.i	7.c	$3$	$6$	$3$	$3.689$	6.0.21870000.1	None		$2$	$0$	$-3$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$
462.2.j.a	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$-1$	$3$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
462.2.j.b	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
462.2.j.c	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-1$	$5$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots$
462.2.j.d	$462$	$2$	462.j	11.c	$5$	$4$	$1$	$3.689$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
462.2.j.e	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.484000000.9	None		$2$	$0$	$-2$	$-2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots$
462.2.j.f	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.64000000.1	None		$2$	$0$	$-2$	$2$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots$
462.2.j.g	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.324000000.3	None		$2$	$0$	$2$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots$
462.2.j.h	$462$	$2$	462.j	11.c	$5$	$8$	$2$	$3.689$	8.0.$\cdots$.8	None		$2$	$0$	$2$	$2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
462.2.k.a	$462$	$2$	462.k	21.g	$6$	$4$	$2$	$3.689$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
462.2.k.b	$462$	$2$	462.k	21.g	$6$	$4$	$2$	$3.689$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
462.2.k.c	$462$	$2$	462.k	21.g	$6$	$4$	$2$	$3.689$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$6$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(2-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
462.2.k.d	$462$	$2$	462.k	21.g	$6$	$8$	$4$	$3.689$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$-12$	$0$	$4$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(-1-\zeta_{24}^{2}+\cdots)q^{3}+\cdots$
462.2.k.e	$462$	$2$	462.k	21.g	$6$	$8$	$4$	$3.689$	$\Q(\zeta_{24})$	None		$2$	$0$	$0$	$4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}-\zeta_{24}^{2}+\cdots)q^{3}+\cdots$
462.2.k.f	$462$	$2$	462.k	21.g	$6$	$8$	$4$	$3.689$	$\Q(\zeta_{24})$	None		$2$	$0$	$0$	$8$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(1-\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
462.2.k.g	$462$	$2$	462.k	21.g	$6$	$20$	$10$	$3.689$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$0$	$-6$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{7}q^{2}-\beta _{12}q^{3}-\beta _{3}q^{4}+(2\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots$
462.2.n.a	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$-2$	$-6$	$3$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
462.2.n.b	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$-2$	$6$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots$
462.2.n.c	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$2$	$-6$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$
462.2.n.d	$462$	$2$	462.n	231.l	$6$	$4$	$2$	$3.689$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$2$	$6$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots$
462.2.n.e	$462$	$2$	462.n	231.l	$6$	$24$	$12$	$3.689$		None		$4$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
462.2.n.f	$462$	$2$	462.n	231.l	$6$	$24$	$12$	$3.689$		None		$4$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
462.2.p.a	$462$	$2$	462.p	77.i	$6$	$16$	$8$	$3.689$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$12$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{13}q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots$
462.2.p.b	$462$	$2$	462.p	77.i	$6$	$16$	$8$	$3.689$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$12$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{12}q^{2}+\beta _{11}q^{3}+(1+\beta _{13})q^{4}+\cdots$
462.2.s.a	$462$	$2$	462.s	231.u	$10$	$128$	$32$	$3.689$		None		$8$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{10}]$
462.2.u.a	$462$	$2$	462.u	77.l	$10$	$32$	$8$	$3.689$		None		$2$	$0$	$0$	$0$	$-10$	$-10$			$\mathrm{SU}(2)[C_{10}]$
462.2.u.b	$462$	$2$	462.u	77.l	$10$	$32$	$8$	$3.689$		None		$2$	$0$	$0$	$0$	$10$	$-10$			$\mathrm{SU}(2)[C_{10}]$

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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.