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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
425.2.a.a	$425$	$2$	425.a	1.a	$1$	$1$	$1$	$3.394$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}+2q^{6}+2q^{7}+3q^{8}+\cdots$
425.2.a.b	$425$	$2$	425.a	1.a	$1$	$1$	$1$	$3.394$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots$
425.2.a.c	$425$	$2$	425.a	1.a	$1$	$1$	$1$	$3.394$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots$
425.2.a.d	$425$	$2$	425.a	1.a	$1$	$1$	$1$	$3.394$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{7}-3q^{8}-3q^{9}+2q^{13}+\cdots$
425.2.a.e	$425$	$2$	425.a	1.a	$1$	$2$	$2$	$3.394$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}+(-3-\beta )q^{6}+\cdots$
425.2.a.f	$425$	$2$	425.a	1.a	$1$	$2$	$2$	$3.394$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$4$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2-\beta )q^{3}+(1+2\beta )q^{4}+\cdots$
425.2.a.g	$425$	$2$	425.a	1.a	$1$	$4$	$4$	$3.394$	4.4.6224.1	None	✓	$1$	$1$	$-2$	$-4$	$0$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots$
425.2.a.h	$425$	$2$	425.a	1.a	$1$	$4$	$4$	$3.394$	4.4.6224.1	None	✓	$1$	$0$	$2$	$4$	$0$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
425.2.a.i	$425$	$2$	425.a	1.a	$1$	$5$	$5$	$3.394$	5.5.1893456.1	None	✓	$1$	$0$	$-1$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots$
425.2.a.j	$425$	$2$	425.a	1.a	$1$	$5$	$5$	$3.394$	5.5.1893456.1	None	✓	$1$	$0$	$1$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots$
425.2.b.a	$425$	$2$	425.b	5.b	$2$	$2$	$2$	$3.394$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots$
425.2.b.b	$425$	$2$	425.b	5.b	$2$	$2$	$2$	$3.394$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}+3q^{9}+\cdots$
425.2.b.c	$425$	$2$	425.b	5.b	$2$	$2$	$2$	$3.394$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-2iq^{7}+\cdots$
425.2.b.d	$425$	$2$	425.b	5.b	$2$	$4$	$4$	$3.394$	$\Q(\zeta_{12})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
425.2.b.e	$425$	$2$	425.b	5.b	$2$	$4$	$4$	$3.394$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-2\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots$
425.2.b.f	$425$	$2$	425.b	5.b	$2$	$10$	$10$	$3.394$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+\beta _{6}q^{3}+(-2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
425.2.c.a	$425$	$2$	425.c	85.c	$2$	$6$	$6$	$3.394$	6.0.350464.1	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$
425.2.c.b	$425$	$2$	425.c	85.c	$2$	$6$	$6$	$3.394$	6.0.350464.1	None		$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$
425.2.c.c	$425$	$2$	425.c	85.c	$2$	$12$	$12$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}-\beta _{2}q^{3}+(-\beta _{1}+\beta _{4})q^{4}+\cdots$
425.2.d.a	$425$	$2$	425.d	17.b	$2$	$6$	$6$	$3.394$	6.0.93924352.2	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}+\beta _{3})q^{4}+\cdots$
425.2.d.b	$425$	$2$	425.d	17.b	$2$	$6$	$6$	$3.394$	6.0.93924352.2	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-\beta _{2}+\beta _{3})q^{4}+\cdots$
425.2.d.c	$425$	$2$	425.d	17.b	$2$	$6$	$6$	$3.394$	6.0.350464.1	None		$2$	$0$	$2$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{4}q^{3}+(\beta _{1}+\beta _{3})q^{4}-\beta _{5}q^{6}+\cdots$
425.2.d.d	$425$	$2$	425.d	17.b	$2$	$8$	$8$	$3.394$	8.0.$\cdots$.3	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(2-\beta _{3})q^{4}+(\beta _{5}+\cdots)q^{6}+\cdots$
425.2.e.a	$425$	$2$	425.e	17.c	$4$	$2$	$1$	$3.394$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-2$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(-1-i)q^{3}+q^{4}+(1-i)q^{6}+\cdots$
425.2.e.b	$425$	$2$	425.e	17.c	$4$	$2$	$1$	$3.394$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{2}+(1+i)q^{3}+q^{4}+(1-i)q^{6}+\cdots$
425.2.e.c	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
425.2.e.d	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}+(\beta _{1}+\beta _{4}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
425.2.e.e	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
425.2.e.f	$425$	$2$	425.e	17.c	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
425.2.j.a	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-4$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{2}-\beta _{4}q^{3}+(1-\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{6}+\cdots$
425.2.j.b	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-4$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}-\beta _{5}q^{3}+(1+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
425.2.j.c	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$4$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(1+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
425.2.j.d	$425$	$2$	425.j	85.j	$4$	$12$	$6$	$3.394$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$4$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{8}q^{2}-\beta _{3}q^{3}+(1-\beta _{2})q^{4}+(1-\beta _{6}+\cdots)q^{6}+\cdots$
425.2.k.a	$425$	$2$	425.k	25.d	$5$	$4$	$1$	$3.394$	$\Q(\zeta_{10})$	None		$2$	$0$	$4$	$1$	$-5$	$14$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots$
425.2.k.b	$425$	$2$	425.k	25.d	$5$	$76$	$19$	$3.394$		None		$2$	$0$	$-6$	$-7$	$13$	$22$			$\mathrm{SU}(2)[C_{5}]$
425.2.k.c	$425$	$2$	425.k	25.d	$5$	$80$	$20$	$3.394$		None		$2$	$0$	$2$	$2$	$0$	$-44$			$\mathrm{SU}(2)[C_{5}]$
425.2.m.a	$425$	$2$	425.m	17.d	$8$	$4$	$1$	$3.394$	$\Q(\zeta_{8})$	None		$2$	$0$	$4$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
425.2.m.b	$425$	$2$	425.m	17.d	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.m.c	$425$	$2$	425.m	17.d	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.m.d	$425$	$2$	425.m	17.d	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.m.e	$425$	$2$	425.m	17.d	$8$	$24$	$6$	$3.394$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.n.a	$425$	$2$	425.n	85.m	$8$	$4$	$1$	$3.394$	$\Q(\zeta_{8})$	None		$2$	$1$	$-4$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\cdots)q^{3}+\cdots$
425.2.n.b	$425$	$2$	425.n	85.m	$8$	$4$	$1$	$3.394$	$\Q(\zeta_{8})$	None		$2$	$0$	$4$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(1-\zeta_{8}+\zeta_{8}^{2})q^{2}+(1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots$
425.2.n.c	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.n.d	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.n.e	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.n.f	$425$	$2$	425.n	85.m	$8$	$24$	$6$	$3.394$		None		$2$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
425.2.p.a	$425$	$2$	425.p	425.p	$10$	$168$	$42$	$3.394$		None		$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
425.2.q.a	$425$	$2$	425.q	425.q	$10$	$176$	$44$	$3.394$		None		$4$	$0$	$-10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
425.2.r.a	$425$	$2$	425.r	25.e	$10$	$160$	$40$	$3.394$		None		$2$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{10}]$

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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.