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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 (41 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
802.2.a.a	$802$	$2$	802.a	1.a	$1$	$1$	$1$	$6.404$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{8}+\cdots$
802.2.a.b	$802$	$2$	802.a	1.a	$1$	$1$	$1$	$6.404$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}-2q^{7}+q^{8}-3q^{9}+\cdots$
802.2.a.c	$802$	$2$	802.a	1.a	$1$	$5$	$5$	$6.404$	5.5.38569.1	None	✓	$1$	$1$	$5$	$-6$	$-9$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{4})q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots$
802.2.a.d	$802$	$2$	802.a	1.a	$1$	$7$	$7$	$6.404$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$6$	$5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{5})q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
802.2.a.e	$802$	$2$	802.a	1.a	$1$	$9$	$9$	$6.404$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-9$	$-6$	$-5$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
802.2.a.f	$802$	$2$	802.a	1.a	$1$	$10$	$10$	$6.404$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$10$	$10$	$9$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{8})q^{5}+\cdots$
802.2.b.a	$802$	$2$	802.b	401.b	$2$	$2$	$2$	$6.404$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+2iq^{3}+q^{4}+4q^{5}-2iq^{6}+\cdots$
802.2.b.b	$802$	$2$	802.b	401.b	$2$	$16$	$16$	$6.404$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-16$	$0$	$-4$	$10$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots$
802.2.b.c	$802$	$2$	802.b	401.b	$2$	$16$	$16$	$6.404$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$16$	$0$	$-4$	$-2$		$2^{3}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$
802.2.c.a	$802$	$2$	802.c	401.c	$4$	$4$	$2$	$6.404$	$\Q(i, \sqrt{10})$	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots$
802.2.c.b	$802$	$2$	802.c	401.c	$4$	$30$	$15$	$6.404$		None		$2$	$0$	$0$	$4$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
802.2.c.c	$802$	$2$	802.c	401.c	$4$	$34$	$17$	$6.404$		None		$2$	$0$	$0$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
802.2.d.a	$802$	$2$	802.d	401.d	$5$	$64$	$16$	$6.404$		None		$2$	$0$	$16$	$5$	$0$	$1$			$\mathrm{SU}(2)[C_{5}]$
802.2.d.b	$802$	$2$	802.d	401.d	$5$	$72$	$18$	$6.404$		None		$2$	$0$	$-18$	$4$	$7$	$-1$			$\mathrm{SU}(2)[C_{5}]$
802.2.e.a	$802$	$2$	802.e	401.e	$8$	$64$	$16$	$6.404$		None		$2$	$0$	$0$	$-8$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
802.2.e.b	$802$	$2$	802.e	401.e	$8$	$68$	$17$	$6.404$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
802.2.f.a	$802$	$2$	802.f	401.f	$10$	$4$	$1$	$6.404$	$\Q(\zeta_{10})$	None		$2$	$1$	$-1$	$-5$	$-1$	$-7$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q-\zeta_{10}^{3}q^{2}+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots$
802.2.f.b	$802$	$2$	802.f	401.f	$10$	$60$	$15$	$6.404$		None		$2$	$0$	$-15$	$0$	$-5$	$4$			$\mathrm{SU}(2)[C_{10}]$
802.2.f.c	$802$	$2$	802.f	401.f	$10$	$72$	$18$	$6.404$		None		$2$	$0$	$18$	$-10$	$1$	$3$			$\mathrm{SU}(2)[C_{10}]$
802.2.h.a	$802$	$2$	802.h	401.h	$20$	$136$	$17$	$6.404$		None		$2$	$0$	$0$	$-2$	$-10$	$-10$			$\mathrm{SU}(2)[C_{20}]$
802.2.h.b	$802$	$2$	802.h	401.h	$20$	$136$	$17$	$6.404$		None		$2$	$0$	$0$	$0$	$12$	$10$			$\mathrm{SU}(2)[C_{20}]$
802.2.i.a	$802$	$2$	802.i	401.i	$25$	$320$	$16$	$6.404$		None		$2$	$0$	$0$	$-5$	$25$	$5$			$\mathrm{SU}(2)[C_{25}]$
802.2.i.b	$802$	$2$	802.i	401.i	$25$	$360$	$18$	$6.404$		None		$2$	$0$	$0$	$-10$	$10$	$-5$			$\mathrm{SU}(2)[C_{25}]$
802.2.j.a	$802$	$2$	802.j	401.j	$40$	$256$	$16$	$6.404$		None		$2$	$0$	$0$	$8$	$8$	$0$			$\mathrm{SU}(2)[C_{40}]$
802.2.j.b	$802$	$2$	802.j	401.j	$40$	$272$	$17$	$6.404$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{40}]$
802.2.k.a	$802$	$2$	802.k	401.k	$50$	$320$	$16$	$6.404$		None		$2$	$0$	$0$	$5$	$-15$	$5$			$\mathrm{SU}(2)[C_{50}]$
802.2.k.b	$802$	$2$	802.k	401.k	$50$	$360$	$18$	$6.404$		None		$2$	$0$	$0$	$10$	$-30$	$-5$			$\mathrm{SU}(2)[C_{50}]$
802.2.m.a	$802$	$2$	802.m	401.m	$100$	$680$	$17$	$6.404$		None		$2$	$0$	$0$	$0$	$-20$	$-10$			$\mathrm{SU}(2)[C_{100}]$
802.2.m.b	$802$	$2$	802.m	401.m	$100$	$680$	$17$	$6.404$		None		$2$	$0$	$0$	$0$	$10$	$10$			$\mathrm{SU}(2)[C_{100}]$
802.2.n.a	$802$	$2$	802.n	401.n	$200$	$1280$	$16$	$6.404$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{200}]$
802.2.n.b	$802$	$2$	802.n	401.n	$200$	$1360$	$17$	$6.404$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{200}]$
802.4.a.a	$802$	$4$	802.a	1.a	$1$	$21$	$21$	$47.320$		None	✓	$1$	$1$	$42$	$-27$	$-64$	$-23$	$-$		$\mathrm{SU}(2)$
802.4.a.b	$802$	$4$	802.a	1.a	$1$	$24$	$24$	$47.320$		None	✓	$1$	$0$	$-48$	$15$	$32$	$23$	$+$		$\mathrm{SU}(2)$
802.4.a.c	$802$	$4$	802.a	1.a	$1$	$26$	$26$	$47.320$		None	✓	$1$	$1$	$-52$	$-21$	$-18$	$-33$	$-$		$\mathrm{SU}(2)$
802.4.a.d	$802$	$4$	802.a	1.a	$1$	$29$	$29$	$47.320$		None	✓	$1$	$0$	$58$	$27$	$66$	$33$	$+$		$\mathrm{SU}(2)$
802.4.b.a	$802$	$4$	802.b	401.b	$2$	$50$	$50$	$47.320$		None		$2$	$0$	$-100$	$0$	$-14$	$38$			$\mathrm{SU}(2)[C_{2}]$
802.4.b.b	$802$	$4$	802.b	401.b	$2$	$50$	$50$	$47.320$		None		$2$	$0$	$100$	$0$	$-2$	$-38$			$\mathrm{SU}(2)[C_{2}]$
802.6.a.a	$802$	$6$	802.a	1.a	$1$	$38$	$38$	$128.628$		None	✓	$1$	$1$	$152$	$-90$	$-305$	$-207$	$+$		$\mathrm{SU}(2)$
802.6.a.b	$802$	$6$	802.a	1.a	$1$	$41$	$41$	$128.628$		None	✓	$1$	$0$	$-164$	$54$	$83$	$207$	$-$		$\mathrm{SU}(2)$
802.6.a.c	$802$	$6$	802.a	1.a	$1$	$43$	$43$	$128.628$		None	✓	$1$	$1$	$-172$	$-54$	$-167$	$-185$	$+$		$\mathrm{SU}(2)$
802.6.a.d	$802$	$6$	802.a	1.a	$1$	$46$	$46$	$128.628$		None	✓	$1$	$0$	$184$	$72$	$345$	$185$	$-$		$\mathrm{SU}(2)$

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