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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 104 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
465.1.u.a	$465$	$1$	465.u	465.u	$6$	$2$	$1$	$0.232$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$		$1$		$q-q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+q^{8}+\cdots$
465.1.u.b	$465$	$1$	465.u	465.u	$6$	$2$	$1$	$0.232$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$		$1$		$q+q^{2}+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}-q^{8}+\cdots$
465.1.x.a	$465$	$1$	465.x	465.x	$10$	$4$	$1$	$0.232$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$4$	$0$		$1$		$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}q^{3}+(\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
465.1.x.b	$465$	$1$	465.x	465.x	$10$	$4$	$1$	$0.232$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$-4$	$0$		$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}q^{3}+(\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
465.1.bl.a	$465$	$1$	465.bl	465.al	$30$	$8$	$1$	$0.232$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$4$	$0$		$1$		$q+(\zeta_{30}^{11}+\zeta_{30}^{13})q^{2}-\zeta_{30}^{8}q^{3}+\cdots$
465.1.bl.b	$465$	$1$	465.bl	465.al	$30$	$8$	$1$	$0.232$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$-4$	$0$		$1$		$q+(-\zeta_{30}^{11}-\zeta_{30}^{13})q^{2}+\zeta_{30}^{8}q^{3}+\cdots$
465.2.a.a	$465$	$2$	465.a	1.a	$1$	$1$	$1$	$3.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
465.2.a.b	$465$	$2$	465.a	1.a	$1$	$1$	$1$	$3.713$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
465.2.a.c	$465$	$2$	465.a	1.a	$1$	$2$	$2$	$3.713$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots$
465.2.a.d	$465$	$2$	465.a	1.a	$1$	$2$	$2$	$3.713$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+(-3+\cdots)q^{7}+\cdots$
465.2.a.e	$465$	$2$	465.a	1.a	$1$	$3$	$3$	$3.713$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-3$	$-3$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
465.2.a.f	$465$	$2$	465.a	1.a	$1$	$3$	$3$	$3.713$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
465.2.a.g	$465$	$2$	465.a	1.a	$1$	$3$	$3$	$3.713$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
465.2.a.h	$465$	$2$	465.a	1.a	$1$	$4$	$4$	$3.713$	4.4.8468.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-4$	$4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots$
465.2.c.a	$465$	$2$	465.c	5.b	$2$	$10$	$10$	$3.713$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}+\beta _{8})q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
465.2.c.b	$465$	$2$	465.c	5.b	$2$	$22$	$22$	$3.713$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
465.2.e.a	$465$	$2$	465.e	93.c	$2$	$44$	$44$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{2}]$
465.2.g.a	$465$	$2$	465.g	465.g	$2$	$4$	$4$	$3.713$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-2-\beta _{2})q^{3}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots$
465.2.g.b	$465$	$2$	465.g	465.g	$2$	$4$	$4$	$3.713$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+3q^{4}-\beta _{1}q^{5}+\beta _{3}q^{6}+\cdots$
465.2.g.c	$465$	$2$	465.g	465.g	$2$	$4$	$4$	$3.713$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(2+\beta _{2})q^{3}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots$
465.2.g.d	$465$	$2$	465.g	465.g	$2$	$8$	$8$	$3.713$	8.0.$\cdots$.6	$_{}$	$\Q(\sqrt{-155}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-2q^{4}+\beta _{4}q^{5}+\beta _{2}q^{9}-2\beta _{1}q^{12}+\cdots$
465.2.g.e	$465$	$2$	465.g	465.g	$2$	$8$	$8$	$3.713$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{24}^{2}q^{2}-\zeta_{24}^{5}q^{3}+q^{4}+(-\zeta_{24}+\cdots)q^{5}+\cdots$
465.2.g.f	$465$	$2$	465.g	465.g	$2$	$32$	$32$	$3.713$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
465.2.i.a	$465$	$2$	465.i	31.c	$3$	$2$	$1$	$3.713$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2q^{4}+\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
465.2.i.b	$465$	$2$	465.i	31.c	$3$	$4$	$2$	$3.713$	$\Q(\sqrt{-3}, \sqrt{97})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{3}-2q^{4}+\beta _{2}q^{5}-\beta _{2}q^{9}+\cdots$
465.2.i.c	$465$	$2$	465.i	31.c	$3$	$6$	$3$	$3.713$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$-4$	$3$	$3$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+(1-\beta _{4})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$
465.2.i.d	$465$	$2$	465.i	31.c	$3$	$8$	$4$	$3.713$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{6}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots$
465.2.i.e	$465$	$2$	465.i	31.c	$3$	$10$	$5$	$3.713$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$-5$	$5$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
465.2.i.f	$465$	$2$	465.i	31.c	$3$	$14$	$7$	$3.713$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$7$	$-7$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{3})q^{4}+\cdots$
465.2.j.a	$465$	$2$	465.j	155.f	$4$	$64$	$32$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{4}]$
465.2.k.a	$465$	$2$	465.k	15.e	$4$	$60$	$30$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
465.2.k.b	$465$	$2$	465.k	15.e	$4$	$60$	$30$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
465.2.n.a	$465$	$2$	465.n	31.d	$5$	$4$	$1$	$3.713$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$-5$	$-1$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2+\zeta_{10}-2\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots$
465.2.n.b	$465$	$2$	465.n	31.d	$5$	$4$	$1$	$3.713$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$1$	$-1$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots$
465.2.n.c	$465$	$2$	465.n	31.d	$5$	$8$	$2$	$3.713$	8.0.13140625.1	$_{}$	None	None		$2$	$0$	$2$	$-2$	$8$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{5}+\beta _{6})q^{2}+\beta _{7}q^{3}+(1+\cdots)q^{4}+\cdots$
465.2.n.d	$465$	$2$	465.n	31.d	$5$	$16$	$4$	$3.713$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$-4$	$-16$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{13}q^{2}-\beta _{5}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots$
465.2.n.e	$465$	$2$	465.n	31.d	$5$	$20$	$5$	$3.713$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$-1$	$5$	$-20$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+\beta _{13}q^{3}+(-\beta _{5}-\beta _{9})q^{4}+\cdots$
465.2.n.f	$465$	$2$	465.n	31.d	$5$	$28$	$7$	$3.713$		$_{}$	None	None		$2$	$0$	$-1$	$7$	$28$	$-7$			$\mathrm{SU}(2)[C_{5}]$
465.2.o.a	$465$	$2$	465.o	93.g	$6$	$84$	$42$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
465.2.q.a	$465$	$2$	465.q	155.j	$6$	$4$	$2$	$3.713$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{3}+2q^{4}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
465.2.q.b	$465$	$2$	465.q	155.j	$6$	$60$	$30$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
465.2.t.a	$465$	$2$	465.t	465.t	$6$	$4$	$2$	$3.713$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-6$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-2-\beta _{2})q^{2}+(2+\beta _{3})q^{3}+(3+3\beta _{2}+\cdots)q^{4}+\cdots$
465.2.t.b	$465$	$2$	465.t	465.t	$6$	$4$	$2$	$3.713$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$6$	$-6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1-\beta _{2})q^{2}+(-2-\beta _{3})q^{3}-3\beta _{2}q^{4}+\cdots$
465.2.t.c	$465$	$2$	465.t	465.t	$6$	$8$	$4$	$3.713$	8.0.3317760000.8	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{4}-2\beta _{5})q^{2}+(-\beta _{5}-\beta _{7})q^{3}+\cdots$
465.2.t.d	$465$	$2$	465.t	465.t	$6$	$104$	$52$	$3.713$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
465.2.w.a	$465$	$2$	465.w	465.w	$10$	$8$	$2$	$3.713$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(-1+\zeta_{15}-\zeta_{15}^{3}+2\zeta_{15}^{4}-\zeta_{15}^{5}+\cdots)q^{2}+\cdots$
465.2.w.b	$465$	$2$	465.w	465.w	$10$	$8$	$2$	$3.713$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{10}]$	$q+(1-\zeta_{15}+\zeta_{15}^{3}-2\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots$
465.2.w.c	$465$	$2$	465.w	465.w	$10$	$224$	$56$	$3.713$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
465.2.y.a	$465$	$2$	465.y	93.k	$10$	$176$	$44$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{10}]$
465.2.ba.a	$465$	$2$	465.ba	155.n	$10$	$128$	$32$	$3.713$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.