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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2004.3.e.a	$2004$	$3$	2004.e	167.b	$2$	$56$	$56$	$54.605$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2010.3.c.a	$2010$	$3$	2010.c	67.b	$2$	$88$	$88$	$54.769$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2012.3.d.a	$2012$	$3$	2012.d	503.b	$2$	$84$	$84$	$54.823$		None		$2$	$0$	$0$	$0$	$0$	$-6$		$\mathrm{SU}(2)[C_{2}]$
2016.3.d.a	$2016$	$3$	2016.d	3.b	$2$	$4$	$4$	$54.932$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{7}-\beta _{2}q^{11}-10q^{13}+14\beta _{1}q^{17}+\cdots$
2016.3.d.b	$2016$	$3$	2016.d	3.b	$2$	$4$	$4$	$54.932$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q-5\beta _{1}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{11}-11\beta _{1}q^{17}+\cdots$
2016.3.d.c	$2016$	$3$	2016.d	3.b	$2$	$4$	$4$	$54.932$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{5}+\beta _{3}q^{7}-3\beta _{2}q^{11}+14q^{13}+\cdots$
2016.3.d.d	$2016$	$3$	2016.d	3.b	$2$	$12$	$12$	$54.932$	12.0.$\cdots$.4	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{5}-\beta _{7})q^{5}-\beta _{1}q^{7}+(\beta _{8}-\beta _{10}+\cdots)q^{11}+\cdots$
2016.3.d.e	$2016$	$3$	2016.d	3.b	$2$	$12$	$12$	$54.932$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}+\beta _{4}q^{7}+\beta _{6}q^{11}+(1+\beta _{9}+\cdots)q^{13}+\cdots$
2016.3.d.f	$2016$	$3$	2016.d	3.b	$2$	$12$	$12$	$54.932$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{5}-\beta _{4}q^{7}-\beta _{6}q^{11}+(1+\beta _{9}+\cdots)q^{13}+\cdots$
2016.3.e.a	$2016$	$3$	2016.e	168.e	$2$	$8$	$8$	$54.932$	$\Q(\zeta_{24})$	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{24}^{6}q^{5}+(3\zeta_{24}+\zeta_{24}^{5})q^{7}+7\zeta_{24}^{2}q^{11}+\cdots$
2016.3.e.b	$2016$	$3$	2016.e	168.e	$2$	$8$	$8$	$54.932$	8.0.157351936.1	$\Q(\sqrt{-7}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2^{16}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+7\beta _{1}q^{7}+(\beta _{3}-\beta _{5})q^{11}+(3\beta _{2}-2\beta _{6}+\cdots)q^{23}+\cdots$
2016.3.e.c	$2016$	$3$	2016.e	168.e	$2$	$48$	$48$	$54.932$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2016.3.f.a	$2016$	$3$	2016.f	7.b	$2$	$8$	$8$	$54.932$	8.0.$\cdots$.8	$\Q(\sqrt{-21}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2^{16}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{5}-7\beta _{1}q^{7}+(\beta _{2}+2\beta _{5})q^{11}+\cdots$
2016.3.f.b	$2016$	$3$	2016.f	7.b	$2$	$8$	$8$	$54.932$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{5}+(-\beta _{2}+\beta _{6})q^{7}+(-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots$
2016.3.f.c	$2016$	$3$	2016.f	7.b	$2$	$8$	$8$	$54.932$	8.0.$\cdots$.3	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+(2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
2016.3.f.d	$2016$	$3$	2016.f	7.b	$2$	$8$	$8$	$54.932$	8.0.$\cdots$.3	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}+3\beta _{4}q^{11}-\beta _{6}q^{13}+\cdots$
2016.3.f.e	$2016$	$3$	2016.f	7.b	$2$	$16$	$16$	$54.932$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{32}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{5}+\beta _{7}q^{7}+(\beta _{7}+\beta _{8}+\beta _{9}+\cdots)q^{11}+\cdots$
2016.3.f.f	$2016$	$3$	2016.f	7.b	$2$	$16$	$16$	$54.932$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{34}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{14}q^{5}+\beta _{11}q^{7}-\beta _{2}q^{11}-\beta _{3}q^{13}+\cdots$
2016.3.f.g	$2016$	$3$	2016.f	7.b	$2$	$16$	$16$	$54.932$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{34}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}-\beta _{8}q^{7}+(\beta _{5}+\beta _{6})q^{11}+(\beta _{7}+\cdots)q^{13}+\cdots$
2016.3.g.a	$2016$	$3$	2016.g	8.d	$2$	$4$	$4$	$54.932$	$\Q(\sqrt{2}, \sqrt{-7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+2\beta _{3})q^{5}+\beta _{3}q^{7}+(4+6\beta _{1}+\cdots)q^{11}+\cdots$
2016.3.g.b	$2016$	$3$	2016.g	8.d	$2$	$8$	$8$	$54.932$	8.0.$\cdots$.3	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2}-\beta _{4})q^{5}+\beta _{2}q^{7}+(-4+\cdots)q^{11}+\cdots$
2016.3.g.c	$2016$	$3$	2016.g	8.d	$2$	$24$	$24$	$54.932$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2016.3.g.d	$2016$	$3$	2016.g	8.d	$2$	$24$	$24$	$54.932$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2016.3.l.a	$2016$	$3$	2016.l	56.h	$2$	$2$	$2$	$54.932$	$\Q(\sqrt{7}) $	$\Q(\sqrt{-14}) $	✓	$4$	$0$	$0$	$0$	$0$	$-14$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}-7q^{7}-\beta q^{13}+7\beta q^{19}-10q^{23}+\cdots$
2016.3.l.b	$2016$	$3$	2016.l	56.h	$2$	$2$	$2$	$54.932$	$\Q(\sqrt{-7}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$0$	$0$	$0$	$-14$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-7q^{7}-\beta q^{11}+18q^{23}-5^{2}q^{25}+\cdots$
2016.3.l.c	$2016$	$3$	2016.l	56.h	$2$	$2$	$2$	$54.932$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-14}) $	✓	$4$	$0$	$0$	$0$	$0$	$14$	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{5}+7q^{7}+3\beta q^{13}+\beta q^{19}-10q^{23}+\cdots$
2016.3.l.d	$2016$	$3$	2016.l	56.h	$2$	$4$	$4$	$54.932$	$\Q(i, \sqrt{6})$	$\Q(\sqrt{-6}) $		$8$	$0$	$0$	$0$	$0$	$20$	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{5}+(5+\beta _{2})q^{7}-5\beta _{1}q^{11}+71q^{25}+\cdots$
2016.3.l.e	$2016$	$3$	2016.l	56.h	$2$	$4$	$4$	$54.932$	$\Q(i, \sqrt{7})$	$\Q(\sqrt{-7}) $		$8$	$0$	$0$	$0$	$0$	$28$	$2^{10}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{7}+\beta _{1}q^{11}-\beta _{2}q^{23}-5^{2}q^{25}+\cdots$
2016.3.l.f	$2016$	$3$	2016.l	56.h	$2$	$8$	$8$	$54.932$	8.0.$\cdots$.51	None		$4$	$0$	$0$	$0$	$0$	$16$	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+\beta _{3})q^{5}+(2+\beta _{4})q^{7}+(\beta _{5}+\cdots)q^{11}+\cdots$
2016.3.l.g	$2016$	$3$	2016.l	56.h	$2$	$24$	$24$	$54.932$		None		$8$	$0$	$0$	$0$	$0$	$-48$		$\mathrm{SU}(2)[C_{2}]$
2016.3.l.h	$2016$	$3$	2016.l	56.h	$2$	$32$	$32$	$54.932$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2016.3.m.a	$2016$	$3$	2016.m	4.b	$2$	$4$	$4$	$54.932$	$\Q(i, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$8$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{2})q^{5}+\beta _{3}q^{7}+(-2\beta _{1}+4\beta _{3})q^{11}+\cdots$
2016.3.m.b	$2016$	$3$	2016.m	4.b	$2$	$8$	$8$	$54.932$	8.0.49787136.1	None		$2$	$0$	$0$	$0$	$-16$	$0$	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{6})q^{5}-\beta _{3}q^{7}+(\beta _{1}-2\beta _{3}+\cdots)q^{11}+\cdots$
2016.3.m.c	$2016$	$3$	2016.m	4.b	$2$	$8$	$8$	$54.932$	8.0.1997017344.2	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+\beta _{5}q^{7}+(-2\beta _{5}+\beta _{6}+\beta _{7})q^{11}+\cdots$
2016.3.m.d	$2016$	$3$	2016.m	4.b	$2$	$12$	$12$	$54.932$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$-16$	$0$	$2^{24}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{5}-\beta _{6}q^{7}+(-\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots$
2016.3.m.e	$2016$	$3$	2016.m	4.b	$2$	$12$	$12$	$54.932$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$16$	$0$	$2^{24}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{5}-\beta _{6}q^{7}+(\beta _{3}-\beta _{6})q^{11}+\cdots$
2016.3.m.f	$2016$	$3$	2016.m	4.b	$2$	$16$	$16$	$54.932$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{42}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+\beta _{4}q^{7}+(-\beta _{4}+\beta _{11})q^{11}+\cdots$
2016.3.n.a	$2016$	$3$	2016.n	24.h	$2$	$48$	$48$	$54.932$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2016.3.o.a	$2016$	$3$	2016.o	84.h	$2$	$32$	$32$	$54.932$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2016.3.o.b	$2016$	$3$	2016.o	84.h	$2$	$32$	$32$	$54.932$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2034.3.b.a	$2034$	$3$	2034.b	3.b	$2$	$36$	$36$	$55.422$		None		$2$	$0$	$0$	$0$	$0$	$-8$		$\mathrm{SU}(2)[C_{2}]$
2034.3.b.b	$2034$	$3$	2034.b	3.b	$2$	$36$	$36$	$55.422$		None		$2$	$0$	$0$	$0$	$0$	$24$		$\mathrm{SU}(2)[C_{2}]$
2034.3.d.a	$2034$	$3$	2034.d	339.c	$2$	$36$	$36$	$55.422$		None		$4$	$0$	$0$	$0$	$0$	$-8$		$\mathrm{SU}(2)[C_{2}]$
2034.3.d.b	$2034$	$3$	2034.d	339.c	$2$	$40$	$40$	$55.422$		None		$4$	$0$	$0$	$0$	$0$	$8$		$\mathrm{SU}(2)[C_{2}]$
2044.3.c.a	$2044$	$3$	2044.c	7.b	$2$	$96$	$96$	$55.695$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2044.3.e.a	$2044$	$3$	2044.e	511.c	$2$	$100$	$100$	$55.695$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
2052.3.e.a	$2052$	$3$	2052.e	3.b	$2$	$12$	$12$	$55.913$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-8$	$2\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-1-\beta _{4})q^{7}-\beta _{6}q^{11}+\cdots$
2052.3.e.b	$2052$	$3$	2052.e	3.b	$2$	$12$	$12$	$55.913$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-8$	$2\cdot 3^{3}\cdot 19$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+\beta _{9}q^{11}+\cdots$
2052.3.e.c	$2052$	$3$	2052.e	3.b	$2$	$24$	$24$	$55.913$		None		$2$	$0$	$0$	$0$	$0$	$8$		$\mathrm{SU}(2)[C_{2}]$
2052.3.h.a	$2052$	$3$	2052.h	19.b	$2$	$2$	$2$	$55.913$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-22$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-11q^{7}+(7-14\zeta_{6})q^{13}+(2^{4}+5\zeta_{6})q^{19}+\cdots$

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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.