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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 173 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
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$
11.3.b.a	$11$	$3$	11.b	11.b	$2$	$1$	$1$	$0.300$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-5$	$-1$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots$
11.3.d.a	$11$	$3$	11.d	11.d	$10$	$4$	$1$	$0.300$	$\Q(\zeta_{10})$	None		$2$	$0$	$-5$	$0$	$-4$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots$
11.4.a.a	$11$	$4$	11.a	1.a	$1$	$2$	$2$	$0.649$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$2$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots$
11.4.c.a	$11$	$4$	11.c	11.c	$5$	$8$	$2$	$0.649$	8.0.$\cdots$.1	None		$2$	$0$	$-7$	$-3$	$-7$	$-35$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots$
11.5.b.a	$11$	$5$	11.b	11.b	$2$	$1$	$1$	$1.137$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$7$	$-49$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots$
11.5.b.b	$11$	$5$	11.b	11.b	$2$	$2$	$2$	$1.137$	$\Q(\sqrt{-30}) $	None		$2$	$0$	$0$	$-6$	$62$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots$
11.5.d.a	$11$	$5$	11.d	11.d	$10$	$12$	$3$	$1.137$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-5$	$-6$	$-18$	$-80$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots$
11.6.a.a	$11$	$6$	11.a	1.a	$1$	$1$	$1$	$1.764$	$\Q$	None	✓	$1$	$1$	$-4$	$-15$	$-19$	$10$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-15q^{3}-2^{4}q^{4}-19q^{5}+60q^{6}+\cdots$
11.6.a.b	$11$	$6$	11.a	1.a	$1$	$3$	$3$	$1.764$	3.3.54492.1	None	✓	$1$	$0$	$0$	$34$	$24$	$84$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(11+\beta _{1}-\beta _{2})q^{3}+(30-6\beta _{1}+\cdots)q^{4}+\cdots$
11.6.c.a	$11$	$6$	11.c	11.c	$5$	$16$	$4$	$1.764$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-1$	$-24$	$-10$	$196$		$2^{4}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{2}+\cdots$
11.7.b.a	$11$	$7$	11.b	11.b	$2$	$1$	$1$	$2.531$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$10$	$74$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+10q^{3}+2^{6}q^{4}+74q^{5}-629q^{9}+\cdots$
11.7.b.b	$11$	$7$	11.b	11.b	$2$	$4$	$4$	$2.531$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None		$2$	$0$	$0$	$24$	$-260$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(6-\beta _{2})q^{3}+(-71+\beta _{2}+\cdots)q^{4}+\cdots$
11.7.d.a	$11$	$7$	11.d	11.d	$10$	$20$	$5$	$2.531$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-5$	$-39$	$181$	$-365$		$2^{4}\cdot 5\cdot 11^{2}$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\beta _{4}+\beta _{6}-\beta _{9})q^{2}+(3\beta _{4}+2\beta _{5}+\cdots)q^{3}+\cdots$
11.8.a.a	$11$	$8$	11.a	1.a	$1$	$2$	$2$	$3.436$	$\Q(\sqrt{15}) $	None	✓	$1$	$1$	$-8$	$-6$	$-470$	$-1228$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-4+\beta )q^{2}+(-3-6\beta )q^{3}+(-52+\cdots)q^{4}+\cdots$
11.8.a.b	$11$	$8$	11.a	1.a	$1$	$4$	$4$	$3.436$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$0$	$-35$	$537$	$170$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-9-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$
11.8.c.a	$11$	$8$	11.c	11.c	$5$	$24$	$6$	$3.436$		None		$2$	$0$	$3$	$36$	$-72$	$68$			$\mathrm{SU}(2)[C_{5}]$
11.9.b.a	$11$	$9$	11.b	11.b	$2$	$1$	$1$	$4.481$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-113$	$1151$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-113q^{3}+2^{8}q^{4}+1151q^{5}+6208q^{9}+\cdots$
11.9.b.b	$11$	$9$	11.b	11.b	$2$	$6$	$6$	$4.481$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$-36$	$-448$	$0$		$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-6-\beta _{4})q^{3}+(-203+3\beta _{3}+\cdots)q^{4}+\cdots$
11.9.d.a	$11$	$9$	11.d	11.d	$10$	$28$	$7$	$4.481$		None		$2$	$0$	$-5$	$144$	$-708$	$5470$			$\mathrm{SU}(2)[C_{10}]$
11.10.a.a	$11$	$10$	11.a	1.a	$1$	$3$	$3$	$5.665$	3.3.2659452.1	None	✓	$1$	$1$	$0$	$-186$	$-1824$	$-7260$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-62+4\beta _{1}-\beta _{2})q^{3}+(304+\cdots)q^{4}+\cdots$
11.10.a.b	$11$	$10$	11.a	1.a	$1$	$5$	$5$	$5.665$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$16$	$112$	$1594$	$8400$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+(3+\beta _{1})q^{2}+(22+3\beta _{1}+\beta _{4})q^{3}+\cdots$
11.10.c.a	$11$	$10$	11.c	11.c	$5$	$32$	$8$	$5.665$		None		$2$	$0$	$-21$	$69$	$225$	$-10675$			$\mathrm{SU}(2)[C_{5}]$
11.11.b.a	$11$	$11$	11.b	11.b	$2$	$1$	$1$	$6.989$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$475$	$-3001$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+475q^{3}+2^{10}q^{4}-3001q^{5}+166576q^{9}+\cdots$
11.11.b.b	$11$	$11$	11.b	11.b	$2$	$8$	$8$	$6.989$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$-402$	$2430$	$0$		$2^{8}\cdot 3^{3}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-50+\beta _{2})q^{3}+(-22^{2}+\cdots)q^{4}+\cdots$
11.11.d.a	$11$	$11$	11.d	11.d	$10$	$36$	$9$	$6.989$		None		$2$	$0$	$-5$	$-78$	$566$	$-9740$			$\mathrm{SU}(2)[C_{10}]$
11.12.a.a	$11$	$12$	11.a	1.a	$1$	$3$	$3$	$8.452$	3.3.202533.1	None	✓	$1$	$1$	$0$	$-393$	$-7305$	$-5082$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots$
11.12.a.b	$11$	$12$	11.a	1.a	$1$	$5$	$5$	$8.452$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$32$	$160$	$-8398$	$79040$	$+$	$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots$
11.12.c.a	$11$	$12$	11.c	11.c	$5$	$40$	$10$	$8.452$		None		$2$	$0$	$11$	$-276$	$6038$	$55440$			$\mathrm{SU}(2)[C_{5}]$
11.13.b.a	$11$	$13$	11.b	11.b	$2$	$1$	$1$	$10.054$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-1358$	$-25774$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-1358q^{3}+2^{12}q^{4}-25774q^{5}+\cdots$
11.13.b.b	$11$	$13$	11.b	11.b	$2$	$10$	$10$	$10.054$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$2436$	$26492$	$0$		$2^{16}\cdot 3^{3}\cdot 11^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(244+\beta _{3})q^{3}+(-2035+\cdots)q^{4}+\cdots$
11.13.d.a	$11$	$13$	11.d	11.d	$10$	$44$	$11$	$10.054$		None		$2$	$0$	$-5$	$-1083$	$-723$	$-219605$			$\mathrm{SU}(2)[C_{10}]$
11.14.a.a	$11$	$14$	11.a	1.a	$1$	$5$	$5$	$11.795$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-64$	$480$	$-454$	$-313920$	$+$	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-13-\beta _{1})q^{2}+(96-2\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots$
11.14.a.b	$11$	$14$	11.a	1.a	$1$	$7$	$7$	$11.795$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$379$	$52689$	$-89386$	$-$	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(54+3\beta _{1}-\beta _{2})q^{3}+(6727+\cdots)q^{4}+\cdots$
11.14.c.a	$11$	$14$	11.c	11.c	$5$	$48$	$12$	$11.795$		None		$2$	$0$	$59$	$-864$	$-52240$	$390696$			$\mathrm{SU}(2)[C_{5}]$
11.15.b.a	$11$	$15$	11.b	11.b	$2$	$1$	$1$	$13.676$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$2515$	$100799$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2515q^{3}+2^{14}q^{4}+100799q^{5}+\cdots$
11.15.b.b	$11$	$15$	11.b	11.b	$2$	$12$	$12$	$13.676$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-5832$	$-135680$	$0$		$2^{22}\cdot 3^{6}\cdot 11^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-486+\beta _{3})q^{3}+(-10877+\cdots)q^{4}+\cdots$
11.15.d.a	$11$	$15$	11.d	11.d	$10$	$52$	$13$	$13.676$		None		$2$	$0$	$-5$	$3312$	$34876$	$1575010$			$\mathrm{SU}(2)[C_{10}]$
11.16.a.a	$11$	$16$	11.a	1.a	$1$	$5$	$5$	$15.696$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-128$	$-5424$	$-458990$	$-2203600$	$-$	$2^{6}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	$q+(-26+\beta _{1})q^{2}+(-1085+\beta _{2})q^{3}+\cdots$
11.16.a.b	$11$	$16$	11.a	1.a	$1$	$7$	$7$	$15.696$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$6142$	$202692$	$-475420$	$+$	$2^{13}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(877-5\beta _{1}+\beta _{2})q^{3}+(18366+\cdots)q^{4}+\cdots$
11.16.c.a	$11$	$16$	11.c	11.c	$5$	$56$	$14$	$15.696$		None		$2$	$0$	$-309$	$5973$	$152073$	$-7602707$			$\mathrm{SU}(2)[C_{5}]$
11.17.b.a	$11$	$17$	11.b	11.b	$2$	$1$	$1$	$17.856$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-353$	$543551$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-353q^{3}+2^{16}q^{4}+543551q^{5}+\cdots$
11.17.b.b	$11$	$17$	11.b	11.b	$2$	$14$	$14$	$17.856$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$498$	$-535618$	$0$		$2^{34}\cdot 3^{10}\cdot 5\cdot 11^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(6^{2}+\beta _{2})q^{3}+(-43414+\cdots)q^{4}+\cdots$
11.17.d.a	$11$	$17$	11.d	11.d	$10$	$60$	$15$	$17.856$		None		$2$	$0$	$-5$	$-150$	$-7938$	$2885320$			$\mathrm{SU}(2)[C_{10}]$
11.18.a.a	$11$	$18$	11.a	1.a	$1$	$6$	$6$	$20.154$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$0$	$11865$	$347991$	$-31314630$	$+$	$2^{12}\cdot 3^{6}\cdot 11$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1977+14\beta _{1}-\beta _{2})q^{3}+\cdots$
11.18.a.b	$11$	$18$	11.a	1.a	$1$	$8$	$8$	$20.154$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$256$	$3058$	$1795234$	$-896364$	$-$	$2^{11}\cdot 3^{5}\cdot 11$	$\mathrm{SU}(2)$	$q+(2^{5}-\beta _{1})q^{2}+(382-9\beta _{1}+\beta _{2})q^{3}+\cdots$
11.18.c.a	$11$	$18$	11.c	11.c	$5$	$64$	$16$	$20.154$		None		$2$	$0$	$795$	$-6360$	$-91530$	$49560700$			$\mathrm{SU}(2)[C_{5}]$
11.19.b.a	$11$	$19$	11.b	11.b	$2$	$1$	$1$	$22.592$	$\Q$	$\Q(\sqrt{-11}) $	✓	$2$	$0$	$0$	$-20870$	$-3063526$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-20870q^{3}+2^{18}q^{4}-3063526q^{5}+\cdots$
11.19.b.b	$11$	$19$	11.b	11.b	$2$	$16$	$16$	$22.592$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$38544$	$5217660$	$0$		$2^{41}\cdot 3^{13}\cdot 11^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2409-\beta _{2})q^{3}+(-136842+\cdots)q^{4}+\cdots$
11.19.d.a	$11$	$19$	11.d	11.d	$10$	$68$	$17$	$22.592$		None		$2$	$0$	$-5$	$-17679$	$-2154139$	$-91602365$			$\mathrm{SU}(2)[C_{10}]$

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