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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 106 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
837.1.d.a	$837$	$1$	837.d	31.b	$2$	$2$	$2$	$0.418$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{93}) $		$4$	$0$	$0$	$0$	$0$	$-2$		$2$		$q-q^{4}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+q^{16}+\cdots$
837.1.k.a	$837$	$1$	837.k	93.h	$6$	$2$	$1$	$0.418$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}-\zeta_{6}q^{19}+\cdots$
837.1.u.a	$837$	$1$	837.u	31.e	$6$	$2$	$1$	$0.418$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-q^{4}-\zeta_{6}^{2}q^{7}+q^{16}-\zeta_{6}^{2}q^{19}+\cdots$
837.1.ba.a	$837$	$1$	837.ba	93.l	$10$	$8$	$2$	$0.418$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}-\zeta_{20}^{7})q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{4}+\cdots)q^{4}+\cdots$
837.1.bo.a	$837$	$1$	837.bo	31.h	$30$	$8$	$1$	$0.418$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{30}^{9}q^{4}+(\zeta_{30}^{2}+\zeta_{30}^{6})q^{7}+(-\zeta_{30}^{2}+\cdots)q^{13}+\cdots$
837.1.by.a	$837$	$1$	837.by	93.o	$30$	$8$	$1$	$0.418$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{2}+\zeta_{30}^{6})q^{7}+(\zeta_{30}^{2}+\cdots)q^{13}+\cdots$
837.2.a.a	$837$	$2$	837.a	1.a	$1$	$2$	$2$	$6.683$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2q^{5}+\cdots$
837.2.a.b	$837$	$2$	837.a	1.a	$1$	$2$	$2$	$6.683$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+2q^{5}+(3-\beta )q^{7}+\cdots$
837.2.a.c	$837$	$2$	837.a	1.a	$1$	$2$	$2$	$6.683$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{4}-\beta q^{5}-q^{7}-\beta q^{11}-q^{13}+\cdots$
837.2.a.d	$837$	$2$	837.a	1.a	$1$	$2$	$2$	$6.683$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}-2q^{5}+(3-\beta )q^{7}+\cdots$
837.2.a.e	$837$	$2$	837.a	1.a	$1$	$2$	$2$	$6.683$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{5}+(1+\cdots)q^{7}+\cdots$
837.2.a.f	$837$	$2$	837.a	1.a	$1$	$3$	$3$	$6.683$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
837.2.a.g	$837$	$2$	837.a	1.a	$1$	$3$	$3$	$6.683$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
837.2.a.h	$837$	$2$	837.a	1.a	$1$	$4$	$4$	$6.683$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{3})q^{7}+\cdots$
837.2.a.i	$837$	$2$	837.a	1.a	$1$	$4$	$4$	$6.683$	$\Q(\sqrt{2}, \sqrt{5})$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
837.2.a.j	$837$	$2$	837.a	1.a	$1$	$5$	$5$	$6.683$	5.5.710984.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
837.2.a.k	$837$	$2$	837.a	1.a	$1$	$5$	$5$	$6.683$	5.5.710984.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
837.2.a.l	$837$	$2$	837.a	1.a	$1$	$6$	$6$	$6.683$	6.6.23493568.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+(1+\beta _{5})q^{7}+\cdots$
837.2.c.a	$837$	$2$	837.c	93.c	$2$	$2$	$2$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}-2\zeta_{6}q^{5}+2q^{7}-\zeta_{6}q^{8}+\cdots$
837.2.c.b	$837$	$2$	837.c	93.c	$2$	$2$	$2$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}-2\zeta_{6}q^{5}+2q^{7}-\zeta_{6}q^{8}+\cdots$
837.2.c.c	$837$	$2$	837.c	93.c	$2$	$2$	$2$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{4}-q^{7}-\zeta_{6}q^{13}+4q^{16}+7q^{19}+\cdots$
837.2.c.d	$837$	$2$	837.c	93.c	$2$	$16$	$16$	$6.683$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{9}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(-1-\beta _{7})q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots$
837.2.c.e	$837$	$2$	837.c	93.c	$2$	$20$	$20$	$6.683$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{9}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{10}q^{2}+(-1-\beta _{7})q^{4}-\beta _{14}q^{5}+\cdots$
837.2.e.a	$837$	$2$	837.e	279.e	$3$	$60$	$30$	$6.683$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{3}]$
837.2.f.a	$837$	$2$	837.f	9.c	$3$	$30$	$15$	$6.683$		$_{}$	None	None		$2$	$0$	$-3$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{3}]$
837.2.f.b	$837$	$2$	837.f	9.c	$3$	$30$	$15$	$6.683$		$_{}$	None	None		$2$	$0$	$5$	$0$	$10$	$0$			$\mathrm{SU}(2)[C_{3}]$
837.2.g.a	$837$	$2$	837.g	279.g	$3$	$60$	$30$	$6.683$		$_{}$	None	None		$2$	$0$	$2$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{3}]$
837.2.h.a	$837$	$2$	837.h	31.c	$3$	$2$	$1$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{3}]$	$q-2q^{4}+(-5+5\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots$
837.2.h.b	$837$	$2$	837.h	31.c	$3$	$16$	$8$	$6.683$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}+(1-\beta _{3})q^{4}-\beta _{8}q^{5}-\beta _{12}q^{7}+\cdots$
837.2.h.c	$837$	$2$	837.h	31.c	$3$	$22$	$11$	$6.683$		$_{}$	None	None		$2$	$0$	$-6$	$0$	$2$	$4$			$\mathrm{SU}(2)[C_{3}]$
837.2.h.d	$837$	$2$	837.h	31.c	$3$	$22$	$11$	$6.683$		$_{}$	None	None		$2$	$0$	$6$	$0$	$-2$	$4$			$\mathrm{SU}(2)[C_{3}]$
837.2.h.e	$837$	$2$	837.h	31.c	$3$	$24$	$12$	$6.683$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{3}]$
837.2.i.a	$837$	$2$	837.i	31.d	$5$	$4$	$1$	$6.683$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$0$	$0$	$-12$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\zeta_{10}^{2}q^{4}-3q^{5}+(-\zeta_{10}-\zeta_{10}^{3})q^{7}+\cdots$
837.2.i.b	$837$	$2$	837.i	31.d	$5$	$4$	$1$	$6.683$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$12$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-2\zeta_{10}^{2}q^{4}+3q^{5}+(-\zeta_{10}-\zeta_{10}^{3})q^{7}+\cdots$
837.2.i.c	$837$	$2$	837.i	31.d	$5$	$8$	$2$	$6.683$	$\Q(\zeta_{15})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$3^{4}$	$\mathrm{U}(1)[D_{5}]$	$q-2\zeta_{15}^{2}q^{4}+(2+\zeta_{15}+\zeta_{15}^{2}-2\zeta_{15}^{3}+\cdots)q^{7}+\cdots$
837.2.i.d	$837$	$2$	837.i	31.d	$5$	$16$	$4$	$6.683$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{13}q^{2}+(-1+\beta _{3}-\beta _{4}-\beta _{6}-2\beta _{10}+\cdots)q^{4}+\cdots$
837.2.i.e	$837$	$2$	837.i	31.d	$5$	$24$	$6$	$6.683$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{5}]$
837.2.i.f	$837$	$2$	837.i	31.d	$5$	$36$	$9$	$6.683$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$7$			$\mathrm{SU}(2)[C_{5}]$
837.2.i.g	$837$	$2$	837.i	31.d	$5$	$36$	$9$	$6.683$		$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$7$			$\mathrm{SU}(2)[C_{5}]$
837.2.i.h	$837$	$2$	837.i	31.d	$5$	$40$	$10$	$6.683$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-10$			$\mathrm{SU}(2)[C_{5}]$
837.2.j.a	$837$	$2$	837.j	93.g	$6$	$2$	$1$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}-q^{4}+(-4+2\zeta_{6})q^{5}+\cdots$
837.2.j.b	$837$	$2$	837.j	93.g	$6$	$2$	$1$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}-q^{4}+(4-2\zeta_{6})q^{5}+\cdots$
837.2.j.c	$837$	$2$	837.j	93.g	$6$	$2$	$1$	$6.683$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+2q^{4}+(-5+5\zeta_{6})q^{7}+(6-3\zeta_{6})q^{13}+\cdots$
837.2.j.d	$837$	$2$	837.j	93.g	$6$	$16$	$8$	$6.683$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(-2-\beta _{1}+\beta _{7})q^{4}-\beta _{3}q^{5}+\cdots$
837.2.j.e	$837$	$2$	837.j	93.g	$6$	$20$	$10$	$6.683$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{11}+\beta _{15})q^{2}+(-1+\beta _{9}+\beta _{13}+\cdots)q^{4}+\cdots$
837.2.j.f	$837$	$2$	837.j	93.g	$6$	$44$	$22$	$6.683$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
837.2.o.a	$837$	$2$	837.o	279.o	$6$	$60$	$30$	$6.683$		$_{}$	None	None		$2$	$0$	$6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
837.2.r.a	$837$	$2$	837.r	279.r	$6$	$60$	$30$	$6.683$		$_{}$	None	None		$2$	$0$	$6$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{6}]$
837.2.s.a	$837$	$2$	837.s	279.s	$6$	$60$	$30$	$6.683$		$_{}$	None	None		$4$	$0$	$6$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{6}]$
837.2.v.a	$837$	$2$	837.v	27.e	$9$	$270$	$45$	$6.683$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$

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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.