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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 81 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
805.1.t.a	$805$	$1$	805.t	805.t	$6$	$2$	$1$	$0.402$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
805.1.t.b	$805$	$1$	805.t	805.t	$6$	$2$	$1$	$0.402$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-115}) $	None		$4$	$0$	$0$	$0$	$1$	$1$		$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
805.2.a.a	$805$	$2$	805.a	1.a	$1$	$1$	$1$	$6.428$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots$
805.2.a.b	$805$	$2$	805.a	1.a	$1$	$1$	$1$	$6.428$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots$
805.2.a.c	$805$	$2$	805.a	1.a	$1$	$1$	$1$	$6.428$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots$
805.2.a.d	$805$	$2$	805.a	1.a	$1$	$1$	$1$	$6.428$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots$
805.2.a.e	$805$	$2$	805.a	1.a	$1$	$2$	$2$	$6.428$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots$
805.2.a.f	$805$	$2$	805.a	1.a	$1$	$3$	$3$	$6.428$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-1+2\beta _{1}-\beta _{2})q^{3}+\cdots$
805.2.a.g	$805$	$2$	805.a	1.a	$1$	$4$	$4$	$6.428$	4.4.2777.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(-1-\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots$
805.2.a.h	$805$	$2$	805.a	1.a	$1$	$4$	$4$	$6.428$	4.4.22545.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots$
805.2.a.i	$805$	$2$	805.a	1.a	$1$	$4$	$4$	$6.428$	4.4.7537.1	$_{}$	None	None	✓	$1$	$0$	$1$	$4$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
805.2.a.j	$805$	$2$	805.a	1.a	$1$	$4$	$4$	$6.428$	4.4.2777.1	$_{}$	None	None	✓	$1$	$0$	$3$	$6$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
805.2.a.k	$805$	$2$	805.a	1.a	$1$	$5$	$5$	$6.428$	5.5.122821.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-6$	$5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots$
805.2.a.l	$805$	$2$	805.a	1.a	$1$	$5$	$5$	$6.428$	5.5.255877.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$-5$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
805.2.a.m	$805$	$2$	805.a	1.a	$1$	$8$	$8$	$6.428$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$7$	$8$	$8$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots$
805.2.c.a	$805$	$2$	805.c	5.b	$2$	$2$	$2$	$6.428$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2q^{4}+(2-i)q^{5}+iq^{7}+2q^{9}+\cdots$
805.2.c.b	$805$	$2$	805.c	5.b	$2$	$24$	$24$	$6.428$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
805.2.c.c	$805$	$2$	805.c	5.b	$2$	$42$	$42$	$6.428$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
805.2.d.a	$805$	$2$	805.d	805.d	$2$	$4$	$4$	$6.428$	$\Q(\sqrt{-5}, \sqrt{23})$	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}-3q^{9}+\cdots$
805.2.d.b	$805$	$2$	805.d	805.d	$2$	$8$	$8$	$6.428$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}-\beta _{5})q^{2}-q^{3}-\beta _{2}q^{4}+(\beta _{3}+2\beta _{7})q^{5}+\cdots$
805.2.d.c	$805$	$2$	805.d	805.d	$2$	$8$	$8$	$6.428$	8.0.40960000.1	$_{}$	None	None		$4$	$0$	$0$	$8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+q^{3}-\beta _{2}q^{4}+(-2\beta _{3}+\cdots)q^{5}+\cdots$
805.2.d.d	$805$	$2$	805.d	805.d	$2$	$12$	$12$	$6.428$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-12$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-q^{3}+(-2-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
805.2.d.e	$805$	$2$	805.d	805.d	$2$	$12$	$12$	$6.428$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$12$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+q^{3}+(-2-\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots$
805.2.d.f	$805$	$2$	805.d	805.d	$2$	$48$	$48$	$6.428$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
805.2.f.a	$805$	$2$	805.f	161.c	$2$	$32$	$32$	$6.428$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$-32$	$-3$			$\mathrm{SU}(2)[C_{2}]$
805.2.f.b	$805$	$2$	805.f	161.c	$2$	$32$	$32$	$6.428$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$32$	$3$			$\mathrm{SU}(2)[C_{2}]$
805.2.i.a	$805$	$2$	805.i	7.c	$3$	$2$	$1$	$6.428$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-2$	$-2$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
805.2.i.b	$805$	$2$	805.i	7.c	$3$	$4$	$2$	$6.428$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
805.2.i.c	$805$	$2$	805.i	7.c	$3$	$24$	$12$	$6.428$		$_{}$	None	None		$2$	$0$	$7$	$2$	$12$	$3$			$\mathrm{SU}(2)[C_{3}]$
805.2.i.d	$805$	$2$	805.i	7.c	$3$	$26$	$13$	$6.428$		$_{}$	None	None		$2$	$0$	$5$	$2$	$-13$	$0$			$\mathrm{SU}(2)[C_{3}]$
805.2.i.e	$805$	$2$	805.i	7.c	$3$	$30$	$15$	$6.428$		$_{}$	None	None		$2$	$0$	$-5$	$0$	$15$	$-3$			$\mathrm{SU}(2)[C_{3}]$
805.2.i.f	$805$	$2$	805.i	7.c	$3$	$34$	$17$	$6.428$		$_{}$	None	None		$2$	$0$	$-5$	$2$	$-17$	$-1$			$\mathrm{SU}(2)[C_{3}]$
805.2.k.a	$805$	$2$	805.k	35.f	$4$	$176$	$88$	$6.428$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
805.2.l.a	$805$	$2$	805.l	115.e	$4$	$144$	$72$	$6.428$		$_{}$	None	None		$4$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
805.2.p.a	$805$	$2$	805.p	161.g	$6$	$64$	$32$	$6.428$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-32$	$3$			$\mathrm{SU}(2)[C_{6}]$
805.2.p.b	$805$	$2$	805.p	161.g	$6$	$64$	$32$	$6.428$		$_{}$	None	None		$2$	$0$	$2$	$0$	$32$	$-3$			$\mathrm{SU}(2)[C_{6}]$
805.2.r.a	$805$	$2$	805.r	805.r	$6$	$8$	$4$	$6.428$	8.0.$\cdots$.4	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{3}q^{4}+(\beta _{4}+\beta _{5})q^{5}+\beta _{1}q^{7}+(3+\cdots)q^{9}+\cdots$
805.2.r.b	$805$	$2$	805.r	805.r	$6$	$176$	$88$	$6.428$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
805.2.s.a	$805$	$2$	805.s	35.j	$6$	$4$	$2$	$6.428$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots$
805.2.s.b	$805$	$2$	805.s	35.j	$6$	$4$	$2$	$6.428$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
805.2.s.c	$805$	$2$	805.s	35.j	$6$	$4$	$2$	$6.428$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$
805.2.s.d	$805$	$2$	805.s	35.j	$6$	$164$	$82$	$6.428$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{6}]$
805.2.u.a	$805$	$2$	805.u	23.c	$11$	$110$	$11$	$6.428$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$11$	$-11$			$\mathrm{SU}(2)[C_{11}]$
805.2.u.b	$805$	$2$	805.u	23.c	$11$	$110$	$11$	$6.428$		$_{}$	None	None		$2$	$0$	$4$	$2$	$-11$	$-11$			$\mathrm{SU}(2)[C_{11}]$
805.2.u.c	$805$	$2$	805.u	23.c	$11$	$130$	$13$	$6.428$		$_{}$	None	None		$2$	$0$	$-2$	$-2$	$13$	$13$			$\mathrm{SU}(2)[C_{11}]$
805.2.u.d	$805$	$2$	805.u	23.c	$11$	$130$	$13$	$6.428$		$_{}$	None	None		$2$	$0$	$2$	$2$	$-13$	$13$			$\mathrm{SU}(2)[C_{11}]$
805.2.v.a	$805$	$2$	805.v	35.k	$12$	$352$	$88$	$6.428$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{12}]$
805.2.y.a	$805$	$2$	805.y	805.y	$12$	$368$	$92$	$6.428$		$_{}$	None	None		$8$	$0$	$-4$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
805.2.bb.a	$805$	$2$	805.bb	161.k	$22$	$320$	$32$	$6.428$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-32$	$-3$			$\mathrm{SU}(2)[C_{22}]$
805.2.bb.b	$805$	$2$	805.bb	161.k	$22$	$320$	$32$	$6.428$		$_{}$	None	None		$2$	$0$	$2$	$0$	$32$	$3$			$\mathrm{SU}(2)[C_{22}]$

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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.