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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 65 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
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
47.2.a.a	$47$	$2$	47.a	1.a	$1$	$4$	$4$	$0.375$	4.4.1957.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
47.2.c.a	$47$	$2$	47.c	47.c	$23$	$66$	$3$	$0.375$		$_{}$	None	None		$2$	$0$	$-21$	$-19$	$-15$	$-19$			$\mathrm{SU}(2)[C_{23}]$
47.3.b.a	$47$	$3$	47.b	47.b	$2$	$2$	$2$	$1.281$	$\Q(\sqrt{-78}) $	$_{}$	None	None		$2$	$0$	$-2$	$-4$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-2q^{3}-3q^{4}+\beta q^{5}+2q^{6}+\cdots$
47.3.b.b	$47$	$3$	47.b	47.b	$2$	$5$	$5$	$1.281$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(4+2\beta _{1}+\cdots)q^{4}+\cdots$
47.3.d.a	$47$	$3$	47.d	47.d	$46$	$154$	$7$	$1.281$		$_{}$	None	None		$2$	$0$	$-21$	$-19$	$-23$	$-15$			$\mathrm{SU}(2)[C_{46}]$
47.4.a.a	$47$	$4$	47.a	1.a	$1$	$3$	$3$	$2.773$	3.3.1101.1	$_{}$	None	None	✓	$1$	$1$	$-5$	$-5$	$-6$	$-45$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots$
47.4.a.b	$47$	$4$	47.a	1.a	$1$	$8$	$8$	$2.773$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$7$	$14$	$39$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(5+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
47.4.c.a	$47$	$4$	47.c	47.c	$23$	$242$	$11$	$2.773$		$_{}$	None	None		$2$	$0$	$-21$	$-25$	$-31$	$-17$			$\mathrm{SU}(2)[C_{23}]$
47.5.b.a	$47$	$5$	47.b	47.b	$2$	$5$	$5$	$4.858$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2\beta _{1}+\beta _{4})q^{2}+(-2\beta _{2}+5\beta _{3})q^{3}+\cdots$
47.5.b.b	$47$	$5$	47.b	47.b	$2$	$10$	$10$	$4.858$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$8$	$0$	$28$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(1+\beta _{9})q^{3}+(2\beta _{3}+\beta _{4}-\beta _{9})q^{4}+\cdots$
47.5.d.a	$47$	$5$	47.d	47.d	$46$	$330$	$15$	$4.858$		$_{}$	None	None		$2$	$0$	$-21$	$-31$	$-23$	$-51$			$\mathrm{SU}(2)[C_{46}]$
47.6.a.a	$47$	$6$	47.a	1.a	$1$	$7$	$7$	$7.538$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-9$	$-20$	$-58$	$-236$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-3+\beta _{3})q^{3}+(7+\cdots)q^{4}+\cdots$
47.6.a.b	$47$	$6$	47.a	1.a	$1$	$12$	$12$	$7.538$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$7$	$16$	$42$	$352$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{4})q^{3}+(18-\beta _{1}+\cdots)q^{4}+\cdots$
47.6.c.a	$47$	$6$	47.c	47.c	$23$	$418$	$19$	$7.538$		$_{}$	None	None		$2$	$0$	$-21$	$-19$	$-7$	$-139$			$\mathrm{SU}(2)[C_{23}]$
47.7.b.a	$47$	$7$	47.b	47.b	$2$	$5$	$5$	$10.813$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{1}-2\beta _{3})q^{2}+(5\beta _{2}-4\beta _{4})q^{3}+(2^{6}+\cdots)q^{4}+\cdots$
47.7.b.b	$47$	$7$	47.b	47.b	$2$	$18$	$18$	$10.813$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$-34$	$0$	$142$		$2^{14}\cdot 3^{3}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-2+\beta _{2})q^{3}+(29+\beta _{2}+\cdots)q^{4}+\cdots$
47.7.d.a	$47$	$7$	47.d	47.d	$46$	$506$	$23$	$10.813$		$_{}$	None	None		$2$	$0$	$-21$	$11$	$-23$	$-165$			$\mathrm{SU}(2)[C_{46}]$
47.8.a.a	$47$	$8$	47.a	1.a	$1$	$11$	$11$	$14.682$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-17$	$-68$	$-56$	$-2256$	$-$	$2^{8}\cdot 3$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{5})q^{3}+\cdots$
47.8.a.b	$47$	$8$	47.a	1.a	$1$	$16$	$16$	$14.682$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$15$	$40$	$444$	$1860$	$+$	$2^{9}\cdot 3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3+\beta _{3})q^{3}+(70-\beta _{1}+\cdots)q^{4}+\cdots$
47.8.c.a	$47$	$8$	47.c	47.c	$23$	$594$	$27$	$14.682$		$_{}$	None	None		$2$	$0$	$-21$	$5$	$-411$	$373$			$\mathrm{SU}(2)[C_{23}]$
47.9.b.a	$47$	$9$	47.b	47.b	$2$	$5$	$5$	$19.147$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{2}+9\beta _{3})q^{2}+(-57\beta _{1}-\beta _{4})q^{3}+\cdots$
47.9.b.b	$47$	$9$	47.b	47.b	$2$	$26$	$26$	$19.147$		$_{}$	None	None		$2$	$0$	$-2$	$68$	$0$	$-2192$			$\mathrm{SU}(2)[C_{2}]$
47.9.d.a	$47$	$9$	47.d	47.d	$46$	$682$	$31$	$19.147$		$_{}$	None	None		$2$	$0$	$-21$	$-91$	$-23$	$2169$			$\mathrm{SU}(2)[C_{46}]$
47.10.a.a	$47$	$10$	47.a	1.a	$1$	$15$	$15$	$24.207$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-33$	$-89$	$-2388$	$-16313$	$+$	$2^{15}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{2}+(-6-\beta _{3})q^{3}+(227+\cdots)q^{4}+\cdots$
47.10.a.b	$47$	$10$	47.a	1.a	$1$	$20$	$20$	$24.207$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$31$	$235$	$112$	$12499$	$-$	$2^{15}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+(12-\beta _{2})q^{3}+(300-2\beta _{1}+\cdots)q^{4}+\cdots$
47.10.c.a	$47$	$10$	47.c	47.c	$23$	$770$	$35$	$24.207$		$_{}$	None	None		$2$	$0$	$-21$	$-169$	$2253$	$3791$			$\mathrm{SU}(2)[C_{23}]$
47.11.b.a	$47$	$11$	47.b	47.b	$2$	$1$	$1$	$29.862$	$\Q$	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$17$	$298$	$0$	$31922$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{2}+298q^{3}-735q^{4}+5066q^{6}+\cdots$
47.11.b.b	$47$	$11$	47.b	47.b	$2$	$4$	$4$	$29.862$	4.4.276125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$-17$	$-298$	$0$	$-31922$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-9\beta _{1}+4\beta _{2})q^{2}+(-11^{2}-11^{2}\beta _{2}+\cdots)q^{3}+\cdots$
47.11.b.c	$47$	$11$	47.b	47.b	$2$	$34$	$34$	$29.862$		$_{}$	None	None		$2$	$0$	$-2$	$-64$	$0$	$3892$			$\mathrm{SU}(2)[C_{2}]$
47.11.d.a	$47$	$11$	47.d	47.d	$46$	$858$	$39$	$29.862$		$_{}$	None	None		$2$	$0$	$-21$	$41$	$-23$	$-3915$			$\mathrm{SU}(2)[C_{46}]$
47.12.a.a	$47$	$12$	47.a	1.a	$1$	$18$	$18$	$36.112$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-41$	$-992$	$-11466$	$-64916$	$-$	$2^{23}\cdot 3^{5}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{2}+(-55+\beta _{2})q^{3}+(881+\cdots)q^{4}+\cdots$
47.12.a.b	$47$	$12$	47.a	1.a	$1$	$23$	$23$	$36.112$		$_{}$	None	None	✓	$1$	$0$	$87$	$-20$	$1034$	$136768$	$+$		$\mathrm{SU}(2)$
47.12.c.a	$47$	$12$	47.c	47.c	$23$	$946$	$43$	$36.112$		$_{}$	None	None		$2$	$0$	$-21$	$485$	$749$	$-38387$			$\mathrm{SU}(2)[C_{23}]$
47.13.b.a	$47$	$13$	47.b	47.b	$2$	$5$	$5$	$42.958$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$5^{2}\cdot 11^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{2}-5\beta _{4})q^{2}+(33\beta _{1}+38\beta _{3})q^{3}+\cdots$
47.13.b.b	$47$	$13$	47.b	47.b	$2$	$42$	$42$	$42.958$		$_{}$	None	None		$2$	$0$	$-2$	$-322$	$0$	$87838$			$\mathrm{SU}(2)[C_{2}]$
47.14.a.a	$47$	$14$	47.a	1.a	$1$	$23$	$23$	$50.399$		$_{}$	None	None	✓	$1$	$1$	$-129$	$-860$	$-10318$	$-708416$	$+$		$\mathrm{SU}(2)$
47.14.a.b	$47$	$14$	47.a	1.a	$1$	$28$	$28$	$50.399$		$_{}$	None	None	✓	$1$	$0$	$127$	$2056$	$52182$	$703372$	$-$		$\mathrm{SU}(2)$
47.15.b.a	$47$	$15$	47.b	47.b	$2$	$5$	$5$	$58.435$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$13^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-33\beta _{1}+4\beta _{4})q^{2}+(-533\beta _{2}-2^{4}\beta _{3}+\cdots)q^{3}+\cdots$
47.15.b.b	$47$	$15$	47.b	47.b	$2$	$50$	$50$	$58.435$		$_{}$	None	None		$2$	$0$	$-2$	$2156$	$0$	$-630008$			$\mathrm{SU}(2)[C_{2}]$
47.16.a.a	$47$	$16$	47.a	1.a	$1$	$26$	$26$	$67.066$		$_{}$	None	None	✓	$1$	$1$	$-473$	$-1745$	$-204476$	$-8691077$	$-$		$\mathrm{SU}(2)$
47.16.a.b	$47$	$16$	47.a	1.a	$1$	$31$	$31$	$67.066$		$_{}$	None	None	✓	$1$	$0$	$39$	$7003$	$108024$	$1191439$	$+$		$\mathrm{SU}(2)$
47.17.b.a	$47$	$17$	47.b	47.b	$2$	$5$	$5$	$76.293$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-43\beta _{1}-98\beta _{4})q^{2}+(3246\beta _{2}+229\beta _{3}+\cdots)q^{3}+\cdots$
47.17.b.b	$47$	$17$	47.b	47.b	$2$	$58$	$58$	$76.293$		$_{}$	None	None		$2$	$0$	$-2$	$-7912$	$0$	$-1154132$			$\mathrm{SU}(2)[C_{2}]$
47.18.a.a	$47$	$18$	47.a	1.a	$1$	$30$	$30$	$86.114$		$_{}$	None	None	✓	$1$	$1$	$15$	$-10640$	$-363048$	$-33054460$	$+$		$\mathrm{SU}(2)$
47.18.a.b	$47$	$18$	47.a	1.a	$1$	$35$	$35$	$86.114$		$_{}$	None	None	✓	$1$	$0$	$1039$	$15604$	$1199452$	$36123152$	$-$		$\mathrm{SU}(2)$
47.19.b.a	$47$	$19$	47.b	47.b	$2$	$5$	$5$	$96.531$	5.5.6903125.1	$_{}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-65\beta _{2}-109\beta _{4})q^{2}+(-2085\beta _{1}+\cdots)q^{3}+\cdots$
47.19.b.b	$47$	$19$	47.b	47.b	$2$	$66$	$66$	$96.531$		$_{}$	None	None		$2$	$0$	$-2$	$20126$	$0$	$36640942$			$\mathrm{SU}(2)[C_{2}]$
47.20.a.a	$47$	$20$	47.a	1.a	$1$	$34$	$34$	$107.544$		$_{}$	None	None	✓	$1$	$1$	$-1481$	$-74552$	$28914$	$-203565056$	$-$		$\mathrm{SU}(2)$
47.20.a.b	$47$	$20$	47.a	1.a	$1$	$39$	$39$	$107.544$		$_{}$	None	None	✓	$1$	$0$	$567$	$4180$	$7841414$	$280678228$	$+$		$\mathrm{SU}(2)$

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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.