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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 (49 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
959.1.d.a	$959$	$1$	959.d	959.d	$2$	$1$	$1$	$0.479$	$\Q$	$D_{3}$	$\Q(\sqrt{-959}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$1$		$1$		$q-q^{2}-q^{3}-q^{5}+q^{6}+q^{7}+q^{8}+\cdots$
959.1.d.b	$959$	$1$	959.d	959.d	$2$	$1$	$1$	$0.479$	$\Q$	$D_{3}$	$\Q(\sqrt{-959}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$1$		$1$		$q-q^{2}+q^{3}+q^{5}-q^{6}+q^{7}+q^{8}+\cdots$
959.1.d.c	$959$	$1$	959.d	959.d	$2$	$1$	$1$	$0.479$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-959}) $	$\Q(\sqrt{137}) $	✓	$4$	$0$	$2$	$0$	$0$	$-1$		$1$		$q+2q^{2}+3q^{4}-q^{7}+4q^{8}-q^{9}-2q^{11}+\cdots$
959.1.d.d	$959$	$1$	959.d	959.d	$2$	$2$	$2$	$0.479$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-959}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$-2$		$1$		$q-q^{2}-\beta q^{3}+\beta q^{5}+\beta q^{6}-q^{7}+q^{8}+\cdots$
959.1.d.e	$959$	$1$	959.d	959.d	$2$	$3$	$3$	$0.479$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-959}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
959.1.d.f	$959$	$1$	959.d	959.d	$2$	$3$	$3$	$0.479$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-959}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$		$1$		$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
959.1.d.g	$959$	$1$	959.d	959.d	$2$	$6$	$6$	$0.479$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-959}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-6$		$1$		$q-\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
959.1.g.a	$959$	$1$	959.g	959.g	$4$	$2$	$1$	$0.479$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+iq^{7}-iq^{9}-iq^{11}+q^{16}+\cdots$
959.1.g.b	$959$	$1$	959.g	959.g	$4$	$4$	$2$	$0.479$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}q^{5}-\zeta_{8}q^{6}+\cdots$
959.1.r.a	$959$	$1$	959.r	959.r	$34$	$16$	$1$	$0.479$	$\Q(\zeta_{34})$	$D_{34}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$		$1$		$q+(\zeta_{34}^{10}-\zeta_{34}^{15})q^{2}+(-\zeta_{34}^{3}+\zeta_{34}^{8}+\cdots)q^{4}+\cdots$
959.1.t.a	$959$	$1$	959.t	959.t	$34$	$16$	$1$	$0.479$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$		$1$		$q+(\zeta_{34}^{2}-\zeta_{34}^{7})q^{2}+(\zeta_{34}^{4}-\zeta_{34}^{9}+\cdots)q^{4}+\cdots$
959.1.v.a	$959$	$1$	959.v	959.v	$68$	$32$	$1$	$0.479$	$\Q(\zeta_{68})$	$D_{68}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{68}^{2}+\zeta_{68}^{20})q^{2}+(\zeta_{68}^{4}-\zeta_{68}^{6}+\cdots)q^{4}+\cdots$
959.2.a.a	$959$	$2$	959.a	1.a	$1$	$2$	$2$	$7.658$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
959.2.a.b	$959$	$2$	959.a	1.a	$1$	$7$	$7$	$7.658$	7.7.28118369.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-3$	$-3$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
959.2.a.c	$959$	$2$	959.a	1.a	$1$	$10$	$10$	$7.658$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$-3$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-\beta _{3}+\beta _{4})q^{4}+\cdots$
959.2.a.d	$959$	$2$	959.a	1.a	$1$	$24$	$24$	$7.658$		$_{}$	None	None	✓	$1$	$0$	$-1$	$7$	$9$	$-24$	$-$		$\mathrm{SU}(2)$
959.2.a.e	$959$	$2$	959.a	1.a	$1$	$26$	$26$	$7.658$		$_{}$	None	None	✓	$1$	$0$	$4$	$3$	$-3$	$26$	$-$		$\mathrm{SU}(2)$
959.2.c.a	$959$	$2$	959.c	137.b	$2$	$2$	$2$	$7.658$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta q^{3}-q^{4}+\beta q^{6}+q^{7}+3q^{8}+\cdots$
959.2.c.b	$959$	$2$	959.c	137.b	$2$	$32$	$32$	$7.658$		$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$32$			$\mathrm{SU}(2)[C_{2}]$
959.2.c.c	$959$	$2$	959.c	137.b	$2$	$36$	$36$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-36$			$\mathrm{SU}(2)[C_{2}]$
959.2.e.a	$959$	$2$	959.e	7.c	$3$	$90$	$45$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$-13$	$-8$	$-1$			$\mathrm{SU}(2)[C_{3}]$
959.2.e.b	$959$	$2$	959.e	7.c	$3$	$90$	$45$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$11$	$4$	$-1$			$\mathrm{SU}(2)[C_{3}]$
959.2.f.a	$959$	$2$	959.f	137.c	$4$	$66$	$33$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
959.2.f.b	$959$	$2$	959.f	137.c	$4$	$70$	$35$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
959.2.i.a	$959$	$2$	959.i	959.i	$6$	$180$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{6}]$
959.2.k.a	$959$	$2$	959.k	959.k	$8$	$8$	$2$	$7.658$	8.0.157351936.1	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{8}]$	$q+(\beta _{1}+\beta _{6})q^{2}+(-1-3\beta _{1}+\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$
959.2.k.b	$959$	$2$	959.k	959.k	$8$	$352$	$88$	$7.658$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
959.2.n.a	$959$	$2$	959.n	959.n	$12$	$360$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
959.2.o.a	$959$	$2$	959.o	137.e	$17$	$544$	$34$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-6$	$34$			$\mathrm{SU}(2)[C_{17}]$
959.2.o.b	$959$	$2$	959.o	137.e	$17$	$576$	$36$	$7.658$		$_{}$	None	None		$2$	$0$	$-6$	$-4$	$-6$	$-36$			$\mathrm{SU}(2)[C_{17}]$
959.2.p.a	$959$	$2$	959.p	959.p	$24$	$720$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$-8$	$-12$	$-12$	$-8$			$\mathrm{SU}(2)[C_{24}]$
959.2.s.a	$959$	$2$	959.s	137.f	$34$	$544$	$34$	$7.658$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-34$			$\mathrm{SU}(2)[C_{34}]$
959.2.s.b	$959$	$2$	959.s	137.f	$34$	$576$	$36$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$36$			$\mathrm{SU}(2)[C_{34}]$
959.2.u.a	$959$	$2$	959.u	959.u	$51$	$2880$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$-17$	$-15$	$-13$	$-15$			$\mathrm{SU}(2)[C_{51}]$
959.2.w.a	$959$	$2$	959.w	137.g	$68$	$1056$	$33$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{68}]$
959.2.w.b	$959$	$2$	959.w	137.g	$68$	$1120$	$35$	$7.658$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-4$	$0$			$\mathrm{SU}(2)[C_{68}]$
959.2.y.a	$959$	$2$	959.y	959.y	$102$	$2880$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$-17$	$-17$	$-17$	$-45$			$\mathrm{SU}(2)[C_{102}]$
959.2.bb.a	$959$	$2$	959.bb	959.ab	$136$	$128$	$2$	$7.658$		$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{136}]$
959.2.bb.b	$959$	$2$	959.bb	959.ab	$136$	$5632$	$88$	$7.658$		$_{}$	None	None		$4$	$0$	$-136$	$0$	$0$	$-64$			$\mathrm{SU}(2)[C_{136}]$
959.2.bc.a	$959$	$2$	959.bc	959.ac	$204$	$5760$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$-34$	$-32$	$-34$	$-68$			$\mathrm{SU}(2)[C_{204}]$
959.2.bf.a	$959$	$2$	959.bf	959.af	$408$	$11520$	$90$	$7.658$		$_{}$	None	None		$4$	$0$	$-60$	$-192$	$-192$	$-128$			$\mathrm{SU}(2)[C_{408}]$
959.4.a.a	$959$	$4$	959.a	1.a	$1$	$40$	$40$	$56.583$		$_{}$	None	None	✓	$1$	$1$	$-10$	$-16$	$-22$	$280$	$-$		$\mathrm{SU}(2)$
959.4.a.b	$959$	$4$	959.a	1.a	$1$	$44$	$44$	$56.583$		$_{}$	None	None	✓	$1$	$1$	$2$	$-14$	$-38$	$-308$	$-$		$\mathrm{SU}(2)$
959.4.a.c	$959$	$4$	959.a	1.a	$1$	$58$	$58$	$56.583$		$_{}$	None	None	✓	$1$	$0$	$-2$	$16$	$22$	$-406$	$+$		$\mathrm{SU}(2)$
959.4.a.d	$959$	$4$	959.a	1.a	$1$	$62$	$62$	$56.583$		$_{}$	None	None	✓	$1$	$0$	$10$	$14$	$38$	$434$	$+$		$\mathrm{SU}(2)$
959.6.a.a	$959$	$6$	959.a	1.a	$1$	$74$	$74$	$153.808$		$_{}$	None	None	✓	$1$	$1$	$-20$	$-49$	$-169$	$3626$	$+$		$\mathrm{SU}(2)$
959.6.a.b	$959$	$6$	959.a	1.a	$1$	$78$	$78$	$153.808$		$_{}$	None	None	✓	$1$	$1$	$4$	$-41$	$-131$	$-3822$	$+$		$\mathrm{SU}(2)$
959.6.a.c	$959$	$6$	959.a	1.a	$1$	$92$	$92$	$153.808$		$_{}$	None	None	✓	$1$	$0$	$-4$	$49$	$169$	$-4508$	$-$		$\mathrm{SU}(2)$
959.6.a.d	$959$	$6$	959.a	1.a	$1$	$96$	$96$	$153.808$		$_{}$	None	None	✓	$1$	$0$	$20$	$41$	$131$	$4704$	$-$		$\mathrm{SU}(2)$

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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.