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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 244 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
210.2.a.a	$210$	$2$	210.a	1.a	$1$	$1$	$1$	$1.677$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
210.2.a.b	$210$	$2$	210.a	1.a	$1$	$1$	$1$	$1.677$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
210.2.a.c	$210$	$2$	210.a	1.a	$1$	$1$	$1$	$1.677$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
210.2.a.d	$210$	$2$	210.a	1.a	$1$	$1$	$1$	$1.677$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
210.2.a.e	$210$	$2$	210.a	1.a	$1$	$1$	$1$	$1.677$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
210.2.b.a	$210$	$2$	210.b	21.c	$2$	$4$	$4$	$1.677$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$-2$	$4$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+q^{5}+\cdots$
210.2.b.b	$210$	$2$	210.b	21.c	$2$	$4$	$4$	$1.677$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$2$	$-4$	$6$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}-q^{5}+\cdots$
210.2.d.a	$210$	$2$	210.d	105.g	$2$	$8$	$8$	$1.677$	8.0.$\cdots$.11	None		$4$	$0$	$-8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{7}q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
210.2.d.b	$210$	$2$	210.d	105.g	$2$	$8$	$8$	$1.677$	8.0.$\cdots$.11	None		$4$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
210.2.g.a	$210$	$2$	210.g	5.b	$2$	$2$	$2$	$1.677$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots$
210.2.g.b	$210$	$2$	210.g	5.b	$2$	$2$	$2$	$1.677$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots$
210.2.i.a	$210$	$2$	210.i	7.c	$3$	$2$	$1$	$1.677$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
210.2.i.b	$210$	$2$	210.i	7.c	$3$	$2$	$1$	$1.677$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
210.2.i.c	$210$	$2$	210.i	7.c	$3$	$2$	$1$	$1.677$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
210.2.i.d	$210$	$2$	210.i	7.c	$3$	$2$	$1$	$1.677$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
210.2.j.a	$210$	$2$	210.j	15.e	$4$	$12$	$6$	$1.677$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$4$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+\beta _{11}q^{3}-\beta _{7}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
210.2.j.b	$210$	$2$	210.j	15.e	$4$	$12$	$6$	$1.677$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$4$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{7}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
210.2.m.a	$210$	$2$	210.m	35.f	$4$	$8$	$4$	$1.677$	8.0.1698758656.6	None		$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+\beta _{3}q^{3}-\beta _{5}q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots$
210.2.m.b	$210$	$2$	210.m	35.f	$4$	$8$	$4$	$1.677$	8.0.1698758656.6	None		$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}-\beta _{3}q^{3}-\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
210.2.n.a	$210$	$2$	210.n	35.j	$6$	$4$	$2$	$1.677$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
210.2.n.b	$210$	$2$	210.n	35.j	$6$	$12$	$6$	$1.677$	12.0.$\cdots$.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{8})q^{3}+(1+\beta _{10})q^{4}+\cdots$
210.2.r.a	$210$	$2$	210.r	21.g	$6$	$12$	$6$	$1.677$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-2$	$6$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(-\beta _{3}+\beta _{9})q^{3}-\beta _{6}q^{4}+\cdots$
210.2.r.b	$210$	$2$	210.r	21.g	$6$	$12$	$6$	$1.677$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$2$	$-6$	$8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}-\beta _{7}q^{3}-\beta _{6}q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots$
210.2.t.a	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$1$	$-2$	$-2$	$-6$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
210.2.t.b	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$-2$	$-1$	$-3$	$10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots$
210.2.t.c	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$2$	$1$	$6$	$-10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
210.2.t.d	$210$	$2$	210.t	105.p	$6$	$4$	$2$	$1.677$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$2$	$2$	$3$	$10$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
210.2.t.e	$210$	$2$	210.t	105.p	$6$	$8$	$4$	$1.677$	8.0.3317760000.3	None		$4$	$0$	$-4$	$0$	$12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
210.2.t.f	$210$	$2$	210.t	105.p	$6$	$8$	$4$	$1.677$	8.0.3317760000.3	None		$4$	$0$	$4$	$0$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(\beta _{5}-\beta _{6})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
210.2.u.a	$210$	$2$	210.u	35.k	$12$	$16$	$4$	$1.677$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$12$	$-8$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{12}q^{2}-\beta _{6}q^{3}+\beta _{5}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
210.2.u.b	$210$	$2$	210.u	35.k	$12$	$16$	$4$	$1.677$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$12$	$-4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{2}q^{2}-\beta _{15}q^{3}-\beta _{5}q^{4}+(1+2\beta _{6}+\cdots)q^{5}+\cdots$
210.2.x.a	$210$	$2$	210.x	105.x	$12$	$64$	$16$	$1.677$		None		$8$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{12}]$
210.3.c.a	$210$	$3$	210.c	15.d	$2$	$24$	$24$	$5.722$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
210.3.e.a	$210$	$3$	210.e	3.b	$2$	$16$	$16$	$5.722$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$-8$	$0$	$0$		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{9}q^{5}+(1+\cdots)q^{6}+\cdots$
210.3.f.a	$210$	$3$	210.f	7.b	$2$	$8$	$8$	$5.722$	8.0.3317760000.3	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+2q^{4}+\beta _{6}q^{5}+\beta _{3}q^{6}+\cdots$
210.3.h.a	$210$	$3$	210.h	35.c	$2$	$16$	$16$	$5.722$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}-\beta _{1}q^{3}-2q^{4}+\beta _{8}q^{5}-\beta _{4}q^{6}+\cdots$
210.3.k.a	$210$	$3$	210.k	105.k	$4$	$32$	$16$	$5.722$		None		$4$	$0$	$-32$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
210.3.k.b	$210$	$3$	210.k	105.k	$4$	$32$	$16$	$5.722$		None		$4$	$0$	$32$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
210.3.l.a	$210$	$3$	210.l	5.c	$4$	$8$	$4$	$5.722$	8.0.$\cdots$.1	None		$2$	$0$	$8$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}+\beta _{7}q^{3}+2\beta _{2}q^{4}+(-2\beta _{3}+\cdots)q^{5}+\cdots$
210.3.l.b	$210$	$3$	210.l	5.c	$4$	$16$	$8$	$5.722$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-16$	$0$	$-16$	$0$		$2^{8}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+2\beta _{2}q^{4}+\cdots$
210.3.o.a	$210$	$3$	210.o	7.d	$6$	$8$	$4$	$5.722$	8.0.3317760000.3	None		$2$	$0$	$0$	$12$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}+\beta _{4})q^{2}+(1+\beta _{3})q^{3}+(-2+2\beta _{3}+\cdots)q^{4}+\cdots$
210.3.o.b	$210$	$3$	210.o	7.d	$6$	$16$	$8$	$5.722$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$-24$	$0$	$4$		$2^{8}\cdot 7$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{9}q^{2}+(-1+\beta _{5})q^{3}+(-2-2\beta _{5}+\cdots)q^{4}+\cdots$
210.3.p.a	$210$	$3$	210.p	35.i	$6$	$32$	$16$	$5.722$		None		$4$	$0$	$0$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{6}]$
210.3.q.a	$210$	$3$	210.q	105.o	$6$	$64$	$32$	$5.722$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
210.3.s.a	$210$	$3$	210.s	21.h	$6$	$40$	$20$	$5.722$		None		$4$	$0$	$0$	$0$	$0$	$20$			$\mathrm{SU}(2)[C_{6}]$
210.3.v.a	$210$	$3$	210.v	35.l	$12$	$32$	$8$	$5.722$		None		$4$	$0$	$-16$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{12}]$
210.3.v.b	$210$	$3$	210.v	35.l	$12$	$32$	$8$	$5.722$		None		$4$	$0$	$16$	$0$	$-8$	$24$			$\mathrm{SU}(2)[C_{12}]$
210.3.w.a	$210$	$3$	210.w	105.w	$12$	$64$	$16$	$5.722$		None		$4$	$0$	$-32$	$-6$	$-12$	$4$			$\mathrm{SU}(2)[C_{12}]$
210.3.w.b	$210$	$3$	210.w	105.w	$12$	$64$	$16$	$5.722$		None		$4$	$0$	$32$	$6$	$12$	$4$			$\mathrm{SU}(2)[C_{12}]$
210.4.a.a	$210$	$4$	210.a	1.a	$1$	$1$	$1$	$12.390$	$\Q$	None	✓	$1$	$1$	$-2$	$-3$	$-5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 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.