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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 68 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
804.1.h.a	$804$	$1$	804.h	804.h	$2$	$1$	$1$	$0.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-201}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
804.1.h.b	$804$	$1$	804.h	804.h	$2$	$1$	$1$	$0.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-201}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
804.1.h.c	$804$	$1$	804.h	804.h	$2$	$1$	$1$	$0.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-201}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
804.1.h.d	$804$	$1$	804.h	804.h	$2$	$1$	$1$	$0.401$	$\Q$	$D_{3}$	$\Q(\sqrt{-201}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
804.1.k.a	$804$	$1$	804.k	201.g	$6$	$2$	$1$	$0.401$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+q^{3}-\zeta_{6}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{19}+\cdots$
804.1.be.a	$804$	$1$	804.be	201.o	$66$	$20$	$1$	$0.401$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q+\zeta_{66}^{30}q^{3}+(-\zeta_{66}^{17}+\zeta_{66}^{26}+\cdots)q^{7}+\cdots$
804.2.a.a	$804$	$2$	804.a	1.a	$1$	$1$	$1$	$6.420$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+3q^{7}+q^{9}-2q^{11}+\cdots$
804.2.a.b	$804$	$2$	804.a	1.a	$1$	$1$	$1$	$6.420$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-2q^{11}-4q^{13}-3q^{17}+\cdots$
804.2.a.c	$804$	$2$	804.a	1.a	$1$	$1$	$1$	$6.420$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+q^{9}+2q^{13}-4q^{15}+\cdots$
804.2.a.d	$804$	$2$	804.a	1.a	$1$	$1$	$1$	$6.420$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
804.2.a.e	$804$	$2$	804.a	1.a	$1$	$3$	$3$	$6.420$	3.3.1076.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$-3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots$
804.2.a.f	$804$	$2$	804.a	1.a	$1$	$5$	$5$	$6.420$	5.5.24571284.1	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots$
804.2.c.a	$804$	$2$	804.c	12.b	$2$	$4$	$4$	$6.420$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-2q^{4}-\zeta_{8}^{2}q^{5}+\cdots$
804.2.c.b	$804$	$2$	804.c	12.b	$2$	$128$	$128$	$6.420$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
804.2.e.a	$804$	$2$	804.e	268.d	$2$	$34$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$-34$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
804.2.e.b	$804$	$2$	804.e	268.d	$2$	$34$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$34$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
804.2.g.a	$804$	$2$	804.g	201.d	$2$	$2$	$2$	$6.420$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots$
804.2.g.b	$804$	$2$	804.g	201.d	$2$	$4$	$4$	$6.420$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots$
804.2.g.c	$804$	$2$	804.g	201.d	$2$	$16$	$16$	$6.420$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{12}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots$
804.2.i.a	$804$	$2$	804.i	67.c	$3$	$2$	$1$	$6.420$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-4$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{3}-2q^{5}+3\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots$
804.2.i.b	$804$	$2$	804.i	67.c	$3$	$2$	$1$	$6.420$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$4$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{3}+2q^{5}-5\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots$
804.2.i.c	$804$	$2$	804.i	67.c	$3$	$2$	$1$	$6.420$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}+2q^{5}+3\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots$
804.2.i.d	$804$	$2$	804.i	67.c	$3$	$8$	$4$	$6.420$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-8$	$2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{3}+\beta _{6}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots$
804.2.i.e	$804$	$2$	804.i	67.c	$3$	$8$	$4$	$6.420$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$8$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}+(-1-\beta _{2}+\beta _{5}-\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots$
804.2.j.a	$804$	$2$	804.j	268.h	$6$	$68$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$-68$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
804.2.j.b	$804$	$2$	804.j	268.h	$6$	$68$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$68$	$0$	$-4$			$\mathrm{SU}(2)[C_{6}]$
804.2.l.a	$804$	$2$	804.l	804.l	$6$	$264$	$132$	$6.420$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
804.2.o.a	$804$	$2$	804.o	201.f	$6$	$2$	$1$	$6.420$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$1$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1+2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{7}+\cdots$
804.2.o.b	$804$	$2$	804.o	201.f	$6$	$4$	$2$	$6.420$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$8$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{3})q^{3}+2q^{5}+(2+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
804.2.o.c	$804$	$2$	804.o	201.f	$6$	$4$	$2$	$6.420$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$-8$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{3})q^{3}-2q^{5}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
804.2.o.d	$804$	$2$	804.o	201.f	$6$	$36$	$18$	$6.420$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
804.2.q.a	$804$	$2$	804.q	67.e	$11$	$60$	$6$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$-2$	$-2$			$\mathrm{SU}(2)[C_{11}]$
804.2.q.b	$804$	$2$	804.q	67.e	$11$	$60$	$6$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$6$	$2$	$2$			$\mathrm{SU}(2)[C_{11}]$
804.2.s.a	$804$	$2$	804.s	201.j	$22$	$20$	$2$	$6.420$	$\Q(\zeta_{33})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{U}(1)[D_{22}]$	$q+\zeta_{33}^{13}q^{3}+(-2\zeta_{33}^{7}-2\zeta_{33}^{8}+\cdots)q^{7}+\cdots$
804.2.s.b	$804$	$2$	804.s	201.j	$22$	$200$	$20$	$6.420$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
804.2.u.a	$804$	$2$	804.u	268.j	$22$	$340$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$-34$	$0$	$-4$			$\mathrm{SU}(2)[C_{22}]$
804.2.u.b	$804$	$2$	804.u	268.j	$22$	$340$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$34$	$0$	$4$			$\mathrm{SU}(2)[C_{22}]$
804.2.w.a	$804$	$2$	804.w	804.w	$22$	$1320$	$132$	$6.420$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
804.2.y.a	$804$	$2$	804.y	67.g	$33$	$100$	$5$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$-10$	$2$	$-3$			$\mathrm{SU}(2)[C_{33}]$
804.2.y.b	$804$	$2$	804.y	67.g	$33$	$120$	$6$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$12$	$-2$	$1$			$\mathrm{SU}(2)[C_{33}]$
804.2.ba.a	$804$	$2$	804.ba	201.p	$66$	$20$	$1$	$6.420$	$\Q(\zeta_{33})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{U}(1)[D_{66}]$	$q+(-2\zeta_{33}-\zeta_{33}^{12})q^{3}+(1-\zeta_{33}+\cdots)q^{7}+\cdots$
804.2.ba.b	$804$	$2$	804.ba	201.p	$66$	$440$	$22$	$6.420$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{66}]$
804.2.bd.a	$804$	$2$	804.bd	804.ad	$66$	$2640$	$132$	$6.420$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{66}]$
804.2.bf.a	$804$	$2$	804.bf	268.n	$66$	$680$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$-68$	$0$	$4$			$\mathrm{SU}(2)[C_{66}]$
804.2.bf.b	$804$	$2$	804.bf	268.n	$66$	$680$	$34$	$6.420$		$_{}$	None	None		$2$	$0$	$0$	$68$	$0$	$-4$			$\mathrm{SU}(2)[C_{66}]$
804.3.b.a	$804$	$3$	804.b	67.b	$2$	$22$	$22$	$21.907$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
804.3.d.a	$804$	$3$	804.d	3.b	$2$	$44$	$44$	$21.907$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
804.3.k.a	$804$	$3$	804.k	201.g	$6$	$2$	$1$	$21.907$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-6$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-3q^{3}+(-2+2\zeta_{6})q^{7}+9q^{9}+\zeta_{6}q^{13}+\cdots$
804.3.k.b	$804$	$3$	804.k	201.g	$6$	$88$	$44$	$21.907$		$_{}$	None	None		$4$	$0$	$0$	$6$	$0$	$8$			$\mathrm{SU}(2)[C_{6}]$
804.3.m.a	$804$	$3$	804.m	67.d	$6$	$22$	$11$	$21.907$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$9$			$\mathrm{SU}(2)[C_{6}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.