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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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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
11.9.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		$2$	$0$	$-5$	$144$	$-708$	$5470$			$\mathrm{SU}(2)[C_{10}]$
12.9.c.a	$12$	$9$	12.c	3.b	$2$	$1$	$1$	$4.889$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$81$	$0$	$4034$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{4}q^{3}+4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots$
12.9.c.b	$12$	$9$	12.c	3.b	$2$	$2$	$2$	$4.889$	$\Q(\sqrt{-110}) $	None		$2$	$0$	$0$	$-102$	$0$	$-6188$		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-51+\beta )q^{3}-18\beta q^{5}-3094q^{7}+\cdots$
12.9.d.a	$12$	$9$	12.d	4.b	$2$	$8$	$8$	$4.889$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$6$	$0$	$-336$	$0$		$2^{22}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots$
13.9.d.a	$13$	$9$	13.d	13.d	$4$	$18$	$9$	$5.296$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$-2$	$-4$	$166$	$5308$		$2^{16}\cdot 3^{2}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+\beta _{6}q^{3}+(-\beta _{1}-142\beta _{2}+\cdots)q^{4}+\cdots$
13.9.f.a	$13$	$9$	13.f	13.f	$12$	$32$	$8$	$5.296$		None		$2$	$0$	$-4$	$-2$	$-172$	$-2784$			$\mathrm{SU}(2)[C_{12}]$
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		$2$	$0$	$-21$	$69$	$225$	$-10675$			$\mathrm{SU}(2)[C_{5}]$
14.9.b.a	$14$	$9$	14.b	7.b	$2$	$4$	$4$	$5.703$	4.0.3520512.3	None		$2$	$0$	$0$	$0$	$0$	$-6076$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{3}q^{2}+(2\beta _{1}-\beta _{2})q^{3}+2^{7}q^{4}+\cdots$
14.9.d.a	$14$	$9$	14.d	7.d	$6$	$12$	$6$	$5.703$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$162$	$1674$	$-1308$		$2^{24}\cdot 3^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{3})q^{2}+(18-9\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
15.9.c.a	$15$	$9$	15.c	3.b	$2$	$10$	$10$	$6.111$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$-112$	$0$	$7156$		$2^{4}\cdot 3^{10}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-11-2\beta _{1}-\beta _{2})q^{3}+(-79+\cdots)q^{4}+\cdots$
15.9.d.a	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$-17$	$-81$	$-625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots$
15.9.d.b	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	$\Q$	$\Q(\sqrt{-15}) $	✓	$2$	$0$	$17$	$81$	$625$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots$
15.9.d.c	$15$	$9$	15.d	15.d	$2$	$12$	$12$	$6.111$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{13}\cdot 3^{18}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots$
15.9.f.a	$15$	$9$	15.f	5.c	$4$	$16$	$8$	$6.111$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$-444$	$4540$		$2^{11}\cdot 3^{20}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{6}q^{3}+(158\beta _{1}-3\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots$
12.10.a.a	$12$	$10$	12.a	1.a	$1$	$1$	$1$	$6.180$	$\Q$	None	✓	$1$	$0$	$0$	$-81$	$990$	$8576$	$-$	$1$	$\mathrm{SU}(2)$	$q-3^{4}q^{3}+990q^{5}+8576q^{7}+3^{8}q^{9}+\cdots$
12.10.b.a	$12$	$10$	12.b	12.b	$2$	$16$	$16$	$6.180$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{68}\cdot 3^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-21-\beta _{1})q^{4}+\cdots$
16.9.c.a	$16$	$9$	16.c	4.b	$2$	$2$	$2$	$6.518$	$\Q(\sqrt{-35}) $	None		$2$	$0$	$0$	$0$	$-1020$	$0$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots$
16.9.c.b	$16$	$9$	16.c	4.b	$2$	$2$	$2$	$6.518$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$516$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots$
16.9.f.a	$16$	$9$	16.f	16.f	$4$	$30$	$15$	$6.518$		None		$2$	$0$	$-2$	$-2$	$-2$	$-4$			$\mathrm{SU}(2)[C_{4}]$
13.10.a.a	$13$	$10$	13.a	1.a	$1$	$4$	$4$	$6.695$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-33$	$-163$	$471$	$-11241$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-8-\beta _{1})q^{2}+(-41+2\beta _{1}-\beta _{3})q^{3}+\cdots$
13.10.a.b	$13$	$10$	13.a	1.a	$1$	$5$	$5$	$6.695$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$15$	$161$	$1803$	$10099$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+(3+\beta _{1})q^{2}+(2^{5}+2\beta _{1}-\beta _{2})q^{3}+\cdots$
13.10.b.a	$13$	$10$	13.b	13.b	$2$	$10$	$10$	$6.695$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2^{7}\cdot 3^{4}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{8}+\beta _{2})q^{4}+\cdots$
13.10.c.a	$13$	$10$	13.c	13.c	$3$	$18$	$9$	$6.695$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$15$	$161$	$-2280$	$-1939$		$2^{16}\cdot 3^{3}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2\beta _{2}-\beta _{3})q^{2}+(-18\beta _{2}-\beta _{6}+\cdots)q^{3}+\cdots$
13.10.e.a	$13$	$10$	13.e	13.e	$6$	$20$	$10$	$6.695$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-3$	$-163$	$0$	$1023$		$2^{22}\cdot 3^{10}\cdot 13^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(2^{4}\beta _{5}-\beta _{6})q^{3}+(2^{8}+\cdots)q^{4}+\cdots$
17.9.e.a	$17$	$9$	17.e	17.e	$16$	$88$	$11$	$6.925$		None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
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		$2$	$0$	$-5$	$-78$	$566$	$-9740$			$\mathrm{SU}(2)[C_{10}]$
14.10.a.a	$14$	$10$	14.a	1.a	$1$	$1$	$1$	$7.211$	$\Q$	None	✓	$1$	$1$	$-16$	$-6$	$560$	$-2401$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots$
14.10.a.b	$14$	$10$	14.a	1.a	$1$	$1$	$1$	$7.211$	$\Q$	None	✓	$1$	$0$	$16$	$170$	$544$	$-2401$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots$
14.10.a.c	$14$	$10$	14.a	1.a	$1$	$2$	$2$	$7.211$	$\Q(\sqrt{2305}) $	None	✓	$1$	$0$	$-32$	$-14$	$-2730$	$4802$	$-$	$2$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots$
14.10.c.a	$14$	$10$	14.c	7.c	$3$	$6$	$3$	$7.211$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$-48$	$-233$	$-733$	$5012$		$2^{6}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2^{4}-2^{4}\beta _{2})q^{2}+(78\beta _{2}-\beta _{3})q^{3}+\cdots$
14.10.c.b	$14$	$10$	14.c	7.c	$3$	$6$	$3$	$7.211$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$48$	$71$	$-1085$	$-6796$		$2^{6}\cdot 7$	$\mathrm{SU}(2)[C_{3}]$	$q+(2^{4}+2^{4}\beta _{1})q^{2}+(-24\beta _{1}-\beta _{3})q^{3}+\cdots$
18.9.b.a	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$-7064$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots$
18.9.b.b	$18$	$9$	18.b	3.b	$2$	$2$	$2$	$7.333$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$0$	$3304$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots$
18.9.d.a	$18$	$9$	18.d	9.d	$6$	$16$	$8$	$7.333$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$126$	$-882$	$-1846$		$2^{28}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(7+2\beta _{1}+\beta _{3}+\beta _{4})q^{3}+\cdots$
12.11.c.a	$12$	$11$	12.c	3.b	$2$	$1$	$1$	$7.624$	$\Q$	$\Q(\sqrt{-3}) $	✓	$2$	$0$	$0$	$-243$	$0$	$22082$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3^{5}q^{3}+22082q^{7}+3^{10}q^{9}+702218q^{13}+\cdots$
12.11.c.b	$12$	$11$	12.c	3.b	$2$	$2$	$2$	$7.624$	$\Q(\sqrt{-35}) $	None		$2$	$0$	$0$	$234$	$0$	$-20636$		$2^{3}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(117+\beta )q^{3}+6\beta q^{5}-10318q^{7}+\cdots$
12.11.d.a	$12$	$11$	12.d	4.b	$2$	$10$	$10$	$7.624$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$22$	$0$	$3116$	$0$		$2^{39}\cdot 3^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{2})q^{2}+\beta _{1}q^{3}+(-65-2\beta _{1}+\cdots)q^{4}+\cdots$
15.10.a.a	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	$\Q$	None	✓	$1$	$1$	$-4$	$81$	$625$	$-7680$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+3^{4}q^{3}-496q^{4}+5^{4}q^{5}+\cdots$
15.10.a.b	$15$	$10$	15.a	1.a	$1$	$1$	$1$	$7.726$	$\Q$	None	✓	$1$	$1$	$22$	$-81$	$-625$	$-5988$	$+$	$1$	$\mathrm{SU}(2)$	$q+22q^{2}-3^{4}q^{3}-28q^{4}-5^{4}q^{5}+\cdots$
15.10.a.c	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	$\Q(\sqrt{4729}) $	None	✓	$1$	$0$	$19$	$162$	$-1250$	$-11872$	$-$	$1$	$\mathrm{SU}(2)$	$q+(10-\beta )q^{2}+3^{4}q^{3}+(770-19\beta )q^{4}+\cdots$
15.10.a.d	$15$	$10$	15.a	1.a	$1$	$2$	$2$	$7.726$	$\Q(\sqrt{241}) $	None	✓	$1$	$0$	$31$	$-162$	$1250$	$14112$	$-$	$3$	$\mathrm{SU}(2)$	$q+(15-\beta )q^{2}-3^{4}q^{3}+(255-31\beta )q^{4}+\cdots$
15.10.b.a	$15$	$10$	15.b	5.b	$2$	$8$	$8$	$7.726$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$-690$	$0$		$2^{3}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(-149-\beta _{1})q^{4}+\cdots$
15.10.e.a	$15$	$10$	15.e	15.e	$4$	$32$	$16$	$7.726$		None		$4$	$0$	$0$	$-150$	$0$	$-9760$			$\mathrm{SU}(2)[C_{4}]$
19.9.b.a	$19$	$9$	19.b	19.b	$2$	$1$	$1$	$7.740$	$\Q$	$\Q(\sqrt{-19}) $	✓	$2$	$0$	$0$	$0$	$-289$	$527$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{4}-17^{2}q^{5}+527q^{7}+3^{8}q^{9}+\cdots$

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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.