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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 59 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
531.1.c.a	$531$	$1$	531.c	59.b	$2$	$1$	$1$	$0.265$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+q^{4}+q^{5}-q^{7}+q^{16}-2q^{17}-q^{19}+\cdots$
531.1.g.a	$531$	$1$	531.g	531.g	$6$	$6$	$3$	$0.265$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
531.2.a.a	$531$	$2$	531.a	1.a	$1$	$2$	$2$	$4.240$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(1-\beta )q^{7}+\cdots$
531.2.a.b	$531$	$2$	531.a	1.a	$1$	$2$	$2$	$4.240$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1-2\beta )q^{5}+\cdots$
531.2.a.c	$531$	$2$	531.a	1.a	$1$	$2$	$2$	$4.240$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$6$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+3q^{5}+(-4+\beta )q^{7}+\cdots$
531.2.a.d	$531$	$2$	531.a	1.a	$1$	$3$	$3$	$4.240$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
531.2.a.e	$531$	$2$	531.a	1.a	$1$	$5$	$5$	$4.240$	5.5.246832.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-8$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
531.2.a.f	$531$	$2$	531.a	1.a	$1$	$5$	$5$	$4.240$	5.5.138136.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{2}+\beta _{3}-\beta _{4})q^{4}+\cdots$
531.2.a.g	$531$	$2$	531.a	1.a	$1$	$5$	$5$	$4.240$	5.5.246832.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$8$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
531.2.d.a	$531$	$2$	531.d	177.d	$2$	$20$	$20$	$4.240$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{12}q^{2}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}-\beta _{4}q^{7}+\cdots$
531.2.e.a	$531$	$2$	531.e	9.c	$3$	$4$	$2$	$4.240$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{6}+\cdots$
531.2.e.b	$531$	$2$	531.e	9.c	$3$	$42$	$21$	$4.240$		$_{}$	None	None		$2$	$0$	$0$	$6$	$-2$	$11$			$\mathrm{SU}(2)[C_{3}]$
531.2.e.c	$531$	$2$	531.e	9.c	$3$	$70$	$35$	$4.240$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-11$			$\mathrm{SU}(2)[C_{3}]$
531.2.f.a	$531$	$2$	531.f	531.f	$6$	$12$	$6$	$4.240$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{7}q^{3}+2\beta _{5}q^{4}+(\beta _{2}+\beta _{10})q^{5}+\cdots$
531.2.f.b	$531$	$2$	531.f	531.f	$6$	$104$	$52$	$4.240$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
531.2.i.a	$531$	$2$	531.i	59.c	$29$	$112$	$4$	$4.240$		$_{}$	None	None		$2$	$0$	$26$	$0$	$25$	$-23$			$\mathrm{SU}(2)[C_{29}]$
531.2.i.b	$531$	$2$	531.i	59.c	$29$	$140$	$5$	$4.240$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$-2$	$-2$			$\mathrm{SU}(2)[C_{29}]$
531.2.i.c	$531$	$2$	531.i	59.c	$29$	$140$	$5$	$4.240$		$_{}$	None	None		$2$	$0$	$1$	$0$	$2$	$-2$			$\mathrm{SU}(2)[C_{29}]$
531.2.i.d	$531$	$2$	531.i	59.c	$29$	$280$	$10$	$4.240$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{29}]$
531.2.j.a	$531$	$2$	531.j	177.f	$58$	$560$	$20$	$4.240$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{58}]$
531.2.m.a	$531$	$2$	531.m	531.m	$87$	$3248$	$58$	$4.240$		$_{}$	None	None		$4$	$0$	$-29$	$-58$	$-25$	$-27$			$\mathrm{SU}(2)[C_{87}]$
531.2.p.a	$531$	$2$	531.p	531.p	$174$	$3248$	$58$	$4.240$		$_{}$	None	None		$4$	$0$	$-87$	$-54$	$-87$	$-27$			$\mathrm{SU}(2)[C_{174}]$
531.3.b.a	$531$	$3$	531.b	3.b	$2$	$40$	$40$	$14.469$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{2}]$
531.3.c.a	$531$	$3$	531.c	59.b	$2$	$3$	$3$	$14.469$	3.3.1593.1	$_{}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
531.3.c.b	$531$	$3$	531.c	59.b	$2$	$6$	$6$	$14.469$	6.0.7196038400.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$6$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-5-\beta _{3}+\beta _{4})q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots$
531.3.c.c	$531$	$3$	531.c	59.b	$2$	$20$	$20$	$14.469$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$2^{11}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{12}q^{7}+\cdots$
531.3.c.d	$531$	$3$	531.c	59.b	$2$	$20$	$20$	$14.469$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}+(-2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
531.4.a.a	$531$	$4$	531.a	1.a	$1$	$2$	$2$	$31.330$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$31$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-4+\beta )q^{4}+(17-3\beta )q^{5}+\cdots$
531.4.a.b	$531$	$4$	531.a	1.a	$1$	$2$	$2$	$31.330$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$4$	$0$	$-6$	$-22$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{2}+(1+4\beta )q^{4}+(-3-2\beta )q^{5}+\cdots$
531.4.a.c	$531$	$4$	531.a	1.a	$1$	$7$	$7$	$31.330$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-59$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(4+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
531.4.a.d	$531$	$4$	531.a	1.a	$1$	$7$	$7$	$31.330$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$8$	$0$	$28$	$-59$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(3+2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
531.4.a.e	$531$	$4$	531.a	1.a	$1$	$8$	$8$	$31.330$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$0$	$-42$	$53$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(5-\beta _{1}+\beta _{2})q^{4}+\cdots$
531.4.a.f	$531$	$4$	531.a	1.a	$1$	$8$	$8$	$31.330$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$12$	$53$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(2-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
531.4.a.g	$531$	$4$	531.a	1.a	$1$	$10$	$10$	$31.330$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-3$	$0$	$-15$	$40$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(6+\beta _{2})q^{4}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
531.4.a.h	$531$	$4$	531.a	1.a	$1$	$14$	$14$	$31.330$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$0$	$-40$	$-26$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots$
531.4.a.i	$531$	$4$	531.a	1.a	$1$	$14$	$14$	$31.330$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$0$	$40$	$-26$	$+$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(4+\beta _{1}+\beta _{2})q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots$
531.4.d.a	$531$	$4$	531.d	177.d	$2$	$60$	$60$	$31.330$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$24$			$\mathrm{SU}(2)[C_{2}]$
531.5.b.a	$531$	$5$	531.b	3.b	$2$	$76$	$76$	$54.889$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-48$			$\mathrm{SU}(2)[C_{2}]$
531.5.c.a	$531$	$5$	531.c	59.b	$2$	$3$	$3$	$54.889$	3.3.1593.1	$_{}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{4}+(2\beta _{1}+9\beta _{2})q^{5}+(7\beta _{1}+15\beta _{2})q^{7}+\cdots$
531.5.c.b	$531$	$5$	531.c	59.b	$2$	$16$	$16$	$54.889$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-82$		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-12+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
531.5.c.c	$531$	$5$	531.c	59.b	$2$	$40$	$40$	$54.889$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$80$			$\mathrm{SU}(2)[C_{2}]$
531.5.c.d	$531$	$5$	531.c	59.b	$2$	$40$	$40$	$54.889$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$80$			$\mathrm{SU}(2)[C_{2}]$
531.6.a.a	$531$	$6$	531.a	1.a	$1$	$9$	$9$	$85.164$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$9$	$0$	$72$	$-208$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(7-2\beta _{1}+\beta _{2})q^{4}+(8+\cdots)q^{5}+\cdots$
531.6.a.b	$531$	$6$	531.a	1.a	$1$	$11$	$11$	$85.164$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$0$	$192$	$-371$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(14-\beta _{1}+\beta _{2})q^{4}+(17+\cdots)q^{5}+\cdots$
531.6.a.c	$531$	$6$	531.a	1.a	$1$	$12$	$12$	$85.164$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-22$	$0$	$-158$	$413$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(17-2\beta _{1}+\beta _{2})q^{4}+\cdots$
531.6.a.d	$531$	$6$	531.a	1.a	$1$	$12$	$12$	$85.164$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$4$	$0$	$-36$	$-411$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(17+\beta _{2})q^{4}+(-3-\beta _{1}+\cdots)q^{5}+\cdots$
531.6.a.e	$531$	$6$	531.a	1.a	$1$	$13$	$13$	$85.164$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$14$	$373$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(19+\beta _{2})q^{4}+(1-\beta _{7})q^{5}+\cdots$
531.6.a.f	$531$	$6$	531.a	1.a	$1$	$15$	$15$	$85.164$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-3$	$0$	$-128$	$282$	$-$	$2^{4}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(20+\beta _{2})q^{4}+(-8-\beta _{1}+\cdots)q^{5}+\cdots$
531.6.a.g	$531$	$6$	531.a	1.a	$1$	$25$	$25$	$85.164$		$_{}$	None	None	✓	$1$	$1$	$-12$	$0$	$-200$	$-38$	$+$		$\mathrm{SU}(2)$
531.6.a.h	$531$	$6$	531.a	1.a	$1$	$25$	$25$	$85.164$		$_{}$	None	None	✓	$1$	$0$	$12$	$0$	$200$	$-38$	$-$		$\mathrm{SU}(2)$

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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.