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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
46.2.a.a	$46$	$2$	46.a	1.a	$1$	$1$	$1$	$0.367$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots$
46.2.c.a	$46$	$2$	46.c	23.c	$11$	$10$	$1$	$0.367$	$\Q(\zeta_{22})$	None		$2$	$0$	$-1$	$-4$	$-6$	$3$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q-\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{7}+\cdots)q^{3}+\cdots$
46.2.c.b	$46$	$2$	46.c	23.c	$11$	$10$	$1$	$0.367$	$\Q(\zeta_{22})$	None		$2$	$0$	$1$	$0$	$-4$	$-7$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\zeta_{22}^{7}+\cdots)q^{3}+\cdots$
46.3.b.a	$46$	$3$	46.b	23.b	$2$	$4$	$4$	$1.253$	4.0.613376.1	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+2q^{4}+\beta _{1}q^{5}+\cdots$
46.3.d.a	$46$	$3$	46.d	23.d	$22$	$40$	$4$	$1.253$		None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
46.4.a.a	$46$	$4$	46.a	1.a	$1$	$1$	$1$	$2.714$	$\Q$	None	✓	$1$	$1$	$-2$	$-1$	$-10$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+4q^{4}-10q^{5}+2q^{6}+\cdots$
46.4.a.b	$46$	$4$	46.a	1.a	$1$	$1$	$1$	$2.714$	$\Q$	None	✓	$1$	$1$	$2$	$-9$	$-20$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-9q^{3}+4q^{4}-20q^{5}-18q^{6}+\cdots$
46.4.a.c	$46$	$4$	46.a	1.a	$1$	$2$	$2$	$2.714$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$-4$	$-1$	$10$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots$
46.4.a.d	$46$	$4$	46.a	1.a	$1$	$2$	$2$	$2.714$	$\Q(\sqrt{73}) $	None	✓	$1$	$0$	$4$	$3$	$10$	$12$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(2-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots$
46.4.c.a	$46$	$4$	46.c	23.c	$11$	$30$	$3$	$2.714$		None		$2$	$0$	$-6$	$6$	$10$	$107$			$\mathrm{SU}(2)[C_{11}]$
46.4.c.b	$46$	$4$	46.c	23.c	$11$	$30$	$3$	$2.714$		None		$2$	$0$	$6$	$2$	$0$	$-115$			$\mathrm{SU}(2)[C_{11}]$
46.5.b.a	$46$	$5$	46.b	23.b	$2$	$8$	$8$	$4.755$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$20$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(3-\beta _{1}+\beta _{3})q^{3}+8q^{4}+\cdots$
46.5.d.a	$46$	$5$	46.d	23.d	$22$	$80$	$8$	$4.755$		None		$2$	$0$	$0$	$-20$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
46.6.a.a	$46$	$6$	46.a	1.a	$1$	$2$	$2$	$7.378$	$\Q(\sqrt{55}) $	None	✓	$1$	$1$	$-8$	$6$	$-68$	$96$	$+$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(3+\beta )q^{3}+2^{4}q^{4}+(-34+\cdots)q^{5}+\cdots$
46.6.a.b	$46$	$6$	46.a	1.a	$1$	$2$	$2$	$7.378$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$8$	$-22$	$-68$	$-312$	$+$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(-11+3\beta )q^{3}+2^{4}q^{4}+(-34+\cdots)q^{5}+\cdots$
46.6.a.c	$46$	$6$	46.a	1.a	$1$	$3$	$3$	$7.378$	3.3.23196.1	None	✓	$1$	$0$	$-12$	$6$	$32$	$-192$	$-$	$2$	$\mathrm{SU}(2)$	$q-4q^{2}+(3+\beta _{1}-2\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
46.6.a.d	$46$	$6$	46.a	1.a	$1$	$3$	$3$	$7.378$	3.3.3149560.1	None	✓	$1$	$0$	$12$	$14$	$82$	$172$	$-$	$2$	$\mathrm{SU}(2)$	$q+4q^{2}+(5-\beta _{1})q^{3}+2^{4}q^{4}+(3^{3}-\beta _{2})q^{5}+\cdots$
46.6.c.a	$46$	$6$	46.c	23.c	$11$	$50$	$5$	$7.378$		None		$2$	$0$	$-20$	$8$	$-14$	$85$			$\mathrm{SU}(2)[C_{11}]$
46.6.c.b	$46$	$6$	46.c	23.c	$11$	$50$	$5$	$7.378$		None		$2$	$0$	$20$	$-12$	$36$	$151$			$\mathrm{SU}(2)[C_{11}]$
46.7.b.a	$46$	$7$	46.b	23.b	$2$	$12$	$12$	$10.582$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-64$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-5-\beta _{1}+\beta _{2})q^{3}+2^{5}q^{4}+\cdots$
46.7.d.a	$46$	$7$	46.d	23.d	$22$	$120$	$12$	$10.582$		None		$2$	$0$	$0$	$64$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
46.8.a.a	$46$	$8$	46.a	1.a	$1$	$2$	$2$	$14.370$	$\Q(\sqrt{85}) $	None	✓	$1$	$1$	$-16$	$-28$	$-110$	$74$	$-$	$2$	$\mathrm{SU}(2)$	$q-8q^{2}+(-14-7\beta )q^{3}+2^{6}q^{4}+(-55+\cdots)q^{5}+\cdots$
46.8.a.b	$46$	$8$	46.a	1.a	$1$	$3$	$3$	$14.370$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$0$	$-24$	$-28$	$390$	$-470$	$+$	$2$	$\mathrm{SU}(2)$	$q-8q^{2}+(-9-\beta _{2})q^{3}+2^{6}q^{4}+(131+\cdots)q^{5}+\cdots$
46.8.a.c	$46$	$8$	46.a	1.a	$1$	$3$	$3$	$14.370$	3.3.285765.1	None	✓	$1$	$1$	$24$	$-12$	$-570$	$-1382$	$-$	$2$	$\mathrm{SU}(2)$	$q+8q^{2}+(-5+2\beta _{1}-\beta _{2})q^{3}+2^{6}q^{4}+\cdots$
46.8.a.d	$46$	$8$	46.a	1.a	$1$	$4$	$4$	$14.370$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$32$	$96$	$180$	$534$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+8q^{2}+(24-\beta _{1})q^{3}+2^{6}q^{4}+(45+\cdots)q^{5}+\cdots$
46.8.c.a	$46$	$8$	46.c	23.c	$11$	$70$	$7$	$14.370$		None		$2$	$0$	$-56$	$-84$	$390$	$-5301$			$\mathrm{SU}(2)[C_{11}]$
46.8.c.b	$46$	$8$	46.c	23.c	$11$	$70$	$7$	$14.370$		None		$2$	$0$	$56$	$32$	$140$	$4513$			$\mathrm{SU}(2)[C_{11}]$
46.9.b.a	$46$	$9$	46.b	23.b	$2$	$16$	$16$	$18.739$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$140$	$0$	$0$		$2^{41}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(9+\beta _{2})q^{3}+2^{7}q^{4}+\beta _{8}q^{5}+\cdots$
46.9.d.a	$46$	$9$	46.d	23.d	$22$	$160$	$16$	$18.739$		None		$2$	$0$	$0$	$-140$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
46.10.a.a	$46$	$10$	46.a	1.a	$1$	$2$	$2$	$23.692$	$\Q(\sqrt{5245}) $	None	✓	$1$	$0$	$-32$	$-60$	$-782$	$-18578$	$-$	$2$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(-30-3\beta )q^{3}+2^{8}q^{4}+\cdots$
46.10.a.b	$46$	$10$	46.a	1.a	$1$	$3$	$3$	$23.692$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$0$	$-48$	$57$	$2544$	$20680$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(19+\beta _{1})q^{3}+2^{8}q^{4}+(847+\cdots)q^{5}+\cdots$
46.10.a.c	$46$	$10$	46.a	1.a	$1$	$3$	$3$	$23.692$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	$1$	$1$	$48$	$-151$	$-1608$	$1090$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+(-50+\beta _{2})q^{3}+2^{8}q^{4}+\cdots$
46.10.a.d	$46$	$10$	46.a	1.a	$1$	$4$	$4$	$23.692$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-64$	$-3$	$-738$	$-1128$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2^{4}q^{2}+(-1+\beta _{1})q^{3}+2^{8}q^{4}+(-185+\cdots)q^{5}+\cdots$
46.10.a.e	$46$	$10$	46.a	1.a	$1$	$4$	$4$	$23.692$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$64$	$173$	$2142$	$7464$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+2^{4}q^{2}+(43+\beta _{1})q^{3}+2^{8}q^{4}+(537+\cdots)q^{5}+\cdots$
46.10.c.a	$46$	$10$	46.c	23.c	$11$	$90$	$9$	$23.692$		None		$2$	$0$	$-144$	$290$	$-2274$	$-28551$			$\mathrm{SU}(2)[C_{11}]$
46.10.c.b	$46$	$10$	46.c	23.c	$11$	$90$	$9$	$23.692$		None		$2$	$0$	$144$	$6$	$-1024$	$20927$			$\mathrm{SU}(2)[C_{11}]$
46.11.b.a	$46$	$11$	46.b	23.b	$2$	$20$	$20$	$29.226$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$-124$	$0$	$0$		$2^{62}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-6+\beta _{1}+\beta _{3})q^{3}+2^{9}q^{4}+\cdots$
46.11.d.a	$46$	$11$	46.d	23.d	$22$	$200$	$20$	$29.226$		None		$2$	$0$	$0$	$124$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
46.12.a.a	$46$	$12$	46.a	1.a	$1$	$5$	$5$	$35.344$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-160$	$230$	$-2740$	$54450$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+(46+\beta _{1})q^{3}+2^{10}q^{4}+(-548+\cdots)q^{5}+\cdots$
46.12.a.b	$46$	$12$	46.a	1.a	$1$	$5$	$5$	$35.344$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$160$	$-210$	$-8990$	$-126430$	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+(-42-\beta _{1})q^{3}+2^{10}q^{4}+\cdots$
46.12.a.c	$46$	$12$	46.a	1.a	$1$	$6$	$6$	$35.344$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$-192$	$230$	$9760$	$-58410$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q-2^{5}q^{2}+(38+\beta _{1})q^{3}+2^{10}q^{4}+(1626+\cdots)q^{5}+\cdots$
46.12.a.d	$46$	$12$	46.a	1.a	$1$	$6$	$6$	$35.344$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$192$	$762$	$9760$	$53658$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q+2^{5}q^{2}+(127-\beta _{1})q^{3}+2^{10}q^{4}+\cdots$
46.12.c.a	$46$	$12$	46.c	23.c	$11$	$110$	$11$	$35.344$		None		$2$	$0$	$-352$	$-552$	$-770$	$286469$			$\mathrm{SU}(2)[C_{11}]$
46.12.c.b	$46$	$12$	46.c	23.c	$11$	$110$	$11$	$35.344$		None		$2$	$0$	$352$	$-460$	$-7020$	$-209737$			$\mathrm{SU}(2)[C_{11}]$
46.13.b.a	$46$	$13$	46.b	23.b	$2$	$24$	$24$	$42.044$		None		$2$	$0$	$0$	$-640$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
46.14.a.a	$46$	$14$	46.a	1.a	$1$	$5$	$5$	$49.326$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-320$	$690$	$-71798$	$31366$	$+$	$2^{9}\cdot 59$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+(138-\beta _{1})q^{3}+2^{12}q^{4}+\cdots$
46.14.a.b	$46$	$14$	46.a	1.a	$1$	$5$	$5$	$49.326$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$320$	$-2746$	$-10358$	$107578$	$+$	$2^{7}$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+(-549+\beta _{2})q^{3}+2^{12}q^{4}+\cdots$
46.14.a.c	$46$	$14$	46.a	1.a	$1$	$6$	$6$	$49.326$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$-384$	$690$	$-9298$	$115714$	$-$	$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q-2^{6}q^{2}+(115-\beta _{1})q^{3}+2^{12}q^{4}+\cdots$
46.14.a.d	$46$	$14$	46.a	1.a	$1$	$6$	$6$	$49.326$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$384$	$170$	$83392$	$493826$	$-$	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+2^{6}q^{2}+(28+\beta _{1})q^{3}+2^{12}q^{4}+(13898+\cdots)q^{5}+\cdots$
46.15.b.a	$46$	$15$	46.b	23.b	$2$	$28$	$28$	$57.191$		None		$2$	$0$	$0$	$4316$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.