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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	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
529.1.d.a	$529$	$1$	529.d	23.d	$22$	$10$	$1$	$0.264$	$\Q(\zeta_{22})$	$D_{3}$	$\Q(\sqrt{-23}) $	None		$20$	$0$	$1$	$1$	$0$	$0$		$1$		$q-\zeta_{22}^{2}q^{2}+\zeta_{22}^{5}q^{3}-\zeta_{22}^{7}q^{6}+\cdots$
529.2.a.a	$529$	$2$	529.a	1.a	$1$	$2$	$2$	$4.224$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
529.2.a.b	$529$	$2$	529.a	1.a	$1$	$2$	$2$	$4.224$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots$
529.2.a.c	$529$	$2$	529.a	1.a	$1$	$2$	$2$	$4.224$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(3+\cdots)q^{6}+\cdots$
529.2.a.d	$529$	$2$	529.a	1.a	$1$	$2$	$2$	$4.224$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
529.2.a.e	$529$	$2$	529.a	1.a	$1$	$2$	$2$	$4.224$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
529.2.a.f	$529$	$2$	529.a	1.a	$1$	$3$	$3$	$4.224$	3.3.621.1	$_{}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots$
529.2.a.g	$529$	$2$	529.a	1.a	$1$	$4$	$4$	$4.224$	$\Q(\zeta_{24})^+$	$_{}$	None	None	✓	$2$	$1$	$-4$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{2})q^{3}-q^{4}-\beta _{3}q^{5}+\cdots$
529.2.a.h	$529$	$2$	529.a	1.a	$1$	$4$	$4$	$4.224$	$\Q(\sqrt{2}, \sqrt{13})$	$_{}$	None	None	✓	$2$	$1$	$-2$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{3})q^{4}+\cdots$
529.2.a.i	$529$	$2$	529.a	1.a	$1$	$5$	$5$	$4.224$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓	$1$	$1$	$2$	$2$	$-7$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{3}-\beta _{4})q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
529.2.a.j	$529$	$2$	529.a	1.a	$1$	$5$	$5$	$4.224$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$7$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{3}-\beta _{4})q^{2}+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
529.2.c.a	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-7$	$-7$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-1+\zeta_{22}+\zeta_{22}^{7}-\zeta_{22}^{8})q^{2}+\cdots$
529.2.c.b	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-7$	$4$	$-3$	$6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-1-\zeta_{22}^{2}-\zeta_{22}^{6}-\zeta_{22}^{8})q^{2}+\cdots$
529.2.c.c	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-7$	$4$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-1-\zeta_{22}^{2}-\zeta_{22}^{6}-\zeta_{22}^{8})q^{2}+\cdots$
529.2.c.d	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$4$	$-7$	$-3$	$6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots$
529.2.c.e	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$4$	$-7$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots$
529.2.c.f	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$4$	$4$	$-8$	$-6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
529.2.c.g	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$4$	$4$	$8$	$6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
529.2.c.h	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$4$	$4$	$-8$	$5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
529.2.c.i	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$4$	$4$	$8$	$-5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
529.2.c.j	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.$\cdots$.6	$_{}$	None	None		$10$	$0$	$-2$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(\beta _{5}+\beta _{16})q^{2}+\beta _{7}q^{3}+(-2\beta _{1}-2\beta _{3}+\cdots)q^{4}+\cdots$
529.2.c.k	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.$\cdots$.6	$_{}$	None	None		$10$	$0$	$-2$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(\beta _{5}+\beta _{16})q^{2}+\beta _{7}q^{3}+(-2\beta _{1}-2\beta _{3}+\cdots)q^{4}+\cdots$
529.2.c.l	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.$\cdots$.3	$_{}$	None	None		$10$	$0$	$0$	$-2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{9}q^{2}+(\beta _{6}+\beta _{17})q^{3}+\beta _{18}q^{4}+\cdots$
529.2.c.m	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.$\cdots$.3	$_{}$	None	None		$10$	$0$	$0$	$-2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{9}q^{2}+(\beta _{6}+\beta _{17})q^{3}+\beta _{18}q^{4}+\cdots$
529.2.c.n	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.$\cdots$.1	$_{}$	None	None		$10$	$0$	$1$	$0$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{16}q^{2}+(1+2\beta _{1}+2\beta _{2}+\beta _{3}-2\beta _{4}+\cdots)q^{3}+\cdots$
529.2.c.o	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.$\cdots$.1	$_{}$	None	None		$10$	$0$	$1$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\beta _{16}q^{2}+(1+2\beta _{1}+2\beta _{2}+\beta _{3}-2\beta _{4}+\cdots)q^{3}+\cdots$
529.2.c.p	$529$	$2$	529.c	23.c	$11$	$30$	$3$	$4.224$		$_{}$	$\Q(\sqrt{-23}) $	None		$20$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{11}]$
529.2.c.q	$529$	$2$	529.c	23.c	$11$	$40$	$4$	$4.224$		$_{}$	None	None		$20$	$0$	$2$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{11}]$
529.2.c.r	$529$	$2$	529.c	23.c	$11$	$40$	$4$	$4.224$		$_{}$	None	None		$20$	$0$	$4$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{11}]$
529.2.e.a	$529$	$2$	529.e	529.e	$23$	$990$	$45$	$4.224$		$_{}$	None	None		$2$	$0$	$-19$	$-19$	$-38$	$-40$			$\mathrm{SU}(2)[C_{23}]$
529.2.g.a	$529$	$2$	529.g	529.g	$253$	$9900$	$45$	$4.224$		$_{}$	None	None		$2$	$0$	$-223$	$-223$	$-204$	$-202$			$\mathrm{SU}(2)[C_{253}]$
529.3.b.a	$529$	$3$	529.b	23.b	$2$	$12$	$12$	$14.414$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-\beta _{1}+\beta _{9})q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots$
529.3.b.b	$529$	$3$	529.b	23.b	$2$	$30$	$30$	$14.414$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
529.3.b.c	$529$	$3$	529.b	23.b	$2$	$32$	$32$	$14.414$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
529.4.a.a	$529$	$4$	529.a	1.a	$1$	$1$	$1$	$31.212$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$6$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-5q^{3}-4q^{4}+6q^{5}+10q^{6}+\cdots$
529.4.a.b	$529$	$4$	529.a	1.a	$1$	$1$	$1$	$31.212$	$\Q$	$_{}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$1$	$3$	$4$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+3q^{2}+4q^{3}+q^{4}+12q^{6}-21q^{8}+\cdots$
529.4.a.c	$529$	$4$	529.a	1.a	$1$	$2$	$2$	$31.212$	$\Q(\sqrt{85}) $	$_{}$	None	None	✓	$2$	$1$	$-4$	$-2$	$0$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}-4q^{4}+\beta q^{5}+2q^{6}+\cdots$
529.4.a.d	$529$	$4$	529.a	1.a	$1$	$2$	$2$	$31.212$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-4$	$-2$	$-16$	$-22$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{2}+(-1+3\beta )q^{3}+(-1+\cdots)q^{4}+\cdots$
529.4.a.e	$529$	$4$	529.a	1.a	$1$	$2$	$2$	$31.212$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-4$	$-2$	$16$	$22$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{2}+(-1+3\beta )q^{3}+(-1+\cdots)q^{4}+\cdots$
529.4.a.f	$529$	$4$	529.a	1.a	$1$	$2$	$2$	$31.212$	$\Q(\sqrt{69}) $	$_{}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$1$	$-3$	$-4$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta )q^{2}+(-3+2\beta )q^{3}+(10+\cdots)q^{4}+\cdots$
529.4.a.g	$529$	$4$	529.a	1.a	$1$	$4$	$4$	$31.212$	4.4.334189.1	$_{}$	None	None	✓	$1$	$1$	$2$	$7$	$-14$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots$
529.4.a.h	$529$	$4$	529.a	1.a	$1$	$5$	$5$	$31.212$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-7$	$-4$	$14$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$
529.4.a.i	$529$	$4$	529.a	1.a	$1$	$5$	$5$	$31.212$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-7$	$4$	$-14$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots$
529.4.a.j	$529$	$4$	529.a	1.a	$1$	$6$	$6$	$31.212$	6.6.$\cdots$.1	$_{}$	None	None	✓	$2$	$1$	$0$	$-6$	$0$	$0$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+(6-\beta _{2}+\cdots)q^{4}+\cdots$
529.4.a.k	$529$	$4$	529.a	1.a	$1$	$12$	$12$	$31.212$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{7}q^{3}+(4+\beta _{2}-\beta _{9})q^{4}+\cdots$
529.4.a.l	$529$	$4$	529.a	1.a	$1$	$24$	$24$	$31.212$		$_{}$	None	None	✓	$2$	$0$	$8$	$24$	$0$	$0$	$+$		$\mathrm{SU}(2)$
529.4.a.m	$529$	$4$	529.a	1.a	$1$	$25$	$25$	$31.212$		$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-51$	$-73$	$-$		$\mathrm{SU}(2)$
529.4.a.n	$529$	$4$	529.a	1.a	$1$	$25$	$25$	$31.212$		$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$51$	$73$	$+$		$\mathrm{SU}(2)$
529.6.a.a	$529$	$6$	529.a	1.a	$1$	$3$	$3$	$84.843$	3.3.7925.1	$_{}$	None	None	✓	$1$	$0$	$-4$	$-20$	$58$	$282$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots$
529.6.a.b	$529$	$6$	529.a	1.a	$1$	$3$	$3$	$84.843$	3.3.621.1	$_{}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-\beta _{1}+3\beta _{2})q^{2}+(-8\beta _{1}+5\beta _{2})q^{3}+\cdots$

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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.