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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
575.1.c.a	$575$	$1$	575.c	115.c	$2$	$2$	$2$	$0.287$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}+iq^{3}+q^{6}-iq^{8}+iq^{13}+\cdots$
575.1.c.b	$575$	$1$	575.c	115.c	$2$	$6$	$6$	$0.287$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
575.1.d.a	$575$	$1$	575.d	23.b	$2$	$1$	$1$	$0.287$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$		$1$		$q+q^{2}+q^{3}+q^{6}-q^{8}+q^{13}-q^{16}+\cdots$
575.1.d.b	$575$	$1$	575.d	23.b	$2$	$3$	$3$	$0.287$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
575.1.d.c	$575$	$1$	575.d	23.b	$2$	$3$	$3$	$0.287$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
575.2.a.a	$575$	$2$	575.a	1.a	$1$	$1$	$1$	$4.591$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+2q^{4}+4q^{6}-q^{7}+\cdots$
575.2.a.b	$575$	$2$	575.a	1.a	$1$	$1$	$1$	$4.591$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}-3q^{9}+2q^{11}+\cdots$
575.2.a.c	$575$	$2$	575.a	1.a	$1$	$1$	$1$	$4.591$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}-3q^{9}-q^{11}+\cdots$
575.2.a.d	$575$	$2$	575.a	1.a	$1$	$1$	$1$	$4.591$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{9}-q^{11}+\cdots$
575.2.a.e	$575$	$2$	575.a	1.a	$1$	$1$	$1$	$4.591$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}+4q^{6}+q^{7}+\cdots$
575.2.a.f	$575$	$2$	575.a	1.a	$1$	$2$	$2$	$4.591$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
575.2.a.g	$575$	$2$	575.a	1.a	$1$	$2$	$2$	$4.591$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots$
575.2.a.h	$575$	$2$	575.a	1.a	$1$	$4$	$4$	$4.591$	4.4.15317.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
575.2.a.i	$575$	$2$	575.a	1.a	$1$	$4$	$4$	$4.591$	4.4.5744.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
575.2.a.j	$575$	$2$	575.a	1.a	$1$	$4$	$4$	$4.591$	4.4.5744.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
575.2.a.k	$575$	$2$	575.a	1.a	$1$	$7$	$7$	$4.591$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
575.2.a.l	$575$	$2$	575.a	1.a	$1$	$7$	$7$	$4.591$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
575.2.b.a	$575$	$2$	575.b	5.b	$2$	$2$	$2$	$4.591$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}-2q^{4}+iq^{7}+3q^{9}+2q^{11}+\cdots$
575.2.b.b	$575$	$2$	575.b	5.b	$2$	$2$	$2$	$4.591$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+3q^{9}+\cdots$
575.2.b.c	$575$	$2$	575.b	5.b	$2$	$4$	$4$	$4.591$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots$
575.2.b.d	$575$	$2$	575.b	5.b	$2$	$4$	$4$	$4.591$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
575.2.b.e	$575$	$2$	575.b	5.b	$2$	$8$	$8$	$4.591$	8.0.$\cdots$.11	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
575.2.b.f	$575$	$2$	575.b	5.b	$2$	$14$	$14$	$4.591$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots$
575.2.e.a	$575$	$2$	575.e	115.e	$4$	$4$	$2$	$4.591$	$\Q(i, \sqrt{46})$	$_{}$	$\Q(\sqrt{-115}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+2\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{2}q^{9}-4q^{16}+\cdots$
575.2.e.b	$575$	$2$	575.e	115.e	$4$	$8$	$4$	$4.591$	8.0.$\cdots$.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{4}-\beta _{7}q^{7}+\beta _{5}q^{8}+\cdots$
575.2.e.c	$575$	$2$	575.e	115.e	$4$	$12$	$6$	$4.591$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	$\Q(\sqrt{-23}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{6}-2\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots$
575.2.e.d	$575$	$2$	575.e	115.e	$4$	$20$	$10$	$4.591$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$4$	$8$	$0$	$0$		$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}-\beta _{2}q^{3}+\beta _{4}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots$
575.2.e.e	$575$	$2$	575.e	115.e	$4$	$24$	$12$	$4.591$		$_{}$	$\Q(\sqrt{-23}) $	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{4}]$
575.2.g.a	$575$	$2$	575.g	25.d	$5$	$4$	$1$	$4.591$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$1$	$-5$	$-5$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
575.2.g.b	$575$	$2$	575.g	25.d	$5$	$108$	$27$	$4.591$		$_{}$	None	None		$2$	$0$	$-4$	$1$	$3$	$24$			$\mathrm{SU}(2)[C_{5}]$
575.2.g.c	$575$	$2$	575.g	25.d	$5$	$112$	$28$	$4.591$		$_{}$	None	None		$2$	$0$	$1$	$4$	$-2$	$-36$			$\mathrm{SU}(2)[C_{5}]$
575.2.i.a	$575$	$2$	575.i	25.e	$10$	$216$	$54$	$4.591$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{10}]$
575.2.k.a	$575$	$2$	575.k	23.c	$11$	$10$	$1$	$4.591$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-5$	$-1$	$0$	$-5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots$
575.2.k.b	$575$	$2$	575.k	23.c	$11$	$10$	$1$	$4.591$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$7$	$7$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1-\zeta_{22}-\zeta_{22}^{7}+\zeta_{22}^{8})q^{2}+(1+\cdots)q^{3}+\cdots$
575.2.k.c	$575$	$2$	575.k	23.c	$11$	$20$	$2$	$4.591$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$-1$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(1-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{6}-\beta _{8}+\beta _{13}+\cdots)q^{2}+\cdots$
575.2.k.d	$575$	$2$	575.k	23.c	$11$	$50$	$5$	$4.591$		$_{}$	None	None		$2$	$0$	$5$	$2$	$0$	$5$			$\mathrm{SU}(2)[C_{11}]$
575.2.k.e	$575$	$2$	575.k	23.c	$11$	$80$	$8$	$4.591$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{11}]$
575.2.k.f	$575$	$2$	575.k	23.c	$11$	$80$	$8$	$4.591$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{11}]$
575.2.k.g	$575$	$2$	575.k	23.c	$11$	$100$	$10$	$4.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{11}]$
575.2.m.a	$575$	$2$	575.m	575.m	$20$	$464$	$58$	$4.591$		$_{}$	None	None		$4$	$0$	$-16$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
575.2.p.a	$575$	$2$	575.p	115.j	$22$	$20$	$2$	$4.591$	$\Q(\zeta_{44})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{22}]$	$q+(-\zeta_{44}^{3}+\zeta_{44}^{5}+\zeta_{44}^{9}+\zeta_{44}^{13}+\cdots)q^{2}+\cdots$
575.2.p.b	$575$	$2$	575.p	115.j	$22$	$20$	$2$	$4.591$	$\Q(\zeta_{44})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{22}]$	$q+(-\zeta_{44}-\zeta_{44}^{5}+\zeta_{44}^{7}+\zeta_{44}^{11}+\cdots)q^{2}+\cdots$
575.2.p.c	$575$	$2$	575.p	115.j	$22$	$40$	$4$	$4.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
575.2.p.d	$575$	$2$	575.p	115.j	$22$	$100$	$10$	$4.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
575.2.p.e	$575$	$2$	575.p	115.j	$22$	$160$	$16$	$4.591$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
575.2.r.a	$575$	$2$	575.r	115.l	$44$	$160$	$8$	$4.591$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
575.2.r.b	$575$	$2$	575.r	115.l	$44$	$200$	$10$	$4.591$		$_{}$	None	None		$4$	$0$	$18$	$14$	$0$	$22$			$\mathrm{SU}(2)[C_{44}]$
575.2.r.c	$575$	$2$	575.r	115.l	$44$	$320$	$16$	$4.591$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{44}]$
575.2.s.a	$575$	$2$	575.s	575.s	$55$	$2320$	$58$	$4.591$		$_{}$	None	None		$4$	$0$	$-27$	$-31$	$-30$	$-76$			$\mathrm{SU}(2)[C_{55}]$
575.2.u.a	$575$	$2$	575.u	575.u	$110$	$2320$	$58$	$4.591$		$_{}$	None	None		$4$	$0$	$-45$	$-45$	$-46$	$0$			$\mathrm{SU}(2)[C_{110}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.