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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
1002.3.c.a	$1002$	$3$	1002.c	167.b	$2$	$56$	$56$	$27.303$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1004.3.d.a	$1004$	$3$	1004.d	251.b	$2$	$14$	$14$	$27.357$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$\Q(\sqrt{-251}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{9}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{11}q^{5}-\beta _{4}q^{7}+(9+\beta _{3}+\cdots)q^{9}+\cdots$
1004.3.d.b	$1004$	$3$	1004.d	251.b	$2$	$28$	$28$	$27.357$		None		$2$	$0$	$0$	$2$	$-4$	$14$		$\mathrm{SU}(2)[C_{2}]$
1005.3.b.a	$1005$	$3$	1005.b	67.b	$2$	$92$	$92$	$27.384$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1006.3.b.a	$1006$	$3$	1006.b	503.b	$2$	$84$	$84$	$27.412$		None		$2$	$0$	$0$	$0$	$0$	$12$		$\mathrm{SU}(2)[C_{2}]$
1008.3.d.a	$1008$	$3$	1008.d	3.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(2\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+(-4\beta _{1}+2\beta _{3})q^{11}+\cdots$
1008.3.d.b	$1008$	$3$	1008.d	3.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$
1008.3.d.c	$1008$	$3$	1008.d	3.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2\beta _{1}-\beta _{2})q^{11}+\cdots$
1008.3.d.d	$1008$	$3$	1008.d	3.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots$
1008.3.d.e	$1008$	$3$	1008.d	3.b	$2$	$8$	$8$	$27.466$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{2}-\beta _{4}+\beta _{5})q^{5}-\beta _{3}q^{7}+(\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots$
1008.3.f.a	$1008$	$3$	1008.f	7.b	$2$	$1$	$1$	$27.466$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$0$	$0$	$0$	$7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+7q^{7}-6q^{11}+18q^{23}+5^{2}q^{25}+\cdots$
1008.3.f.b	$1008$	$3$	1008.f	7.b	$2$	$2$	$2$	$27.466$	$\Q(\sqrt{7}) $	$\Q(\sqrt{-7}) $	✓	$4$	$0$	$0$	$0$	$0$	$-14$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-7q^{7}+\beta q^{11}-2\beta q^{23}+5^{2}q^{25}+\cdots$
1008.3.f.c	$1008$	$3$	1008.f	7.b	$2$	$2$	$2$	$27.466$	$\Q(\sqrt{-6}) $	None		$2$	$0$	$0$	$0$	$0$	$-10$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+(-5+\beta )q^{7}-6q^{11}+\beta q^{13}+\cdots$
1008.3.f.d	$1008$	$3$	1008.f	7.b	$2$	$2$	$2$	$27.466$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$0$	$-2$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+10q^{11}+\cdots$
1008.3.f.e	$1008$	$3$	1008.f	7.b	$2$	$2$	$2$	$27.466$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$2$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+(1-\zeta_{6})q^{7}+2\zeta_{6}q^{13}-4\zeta_{6}q^{19}+\cdots$
1008.3.f.f	$1008$	$3$	1008.f	7.b	$2$	$2$	$2$	$27.466$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$0$	$14$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{5}+7q^{7}+18q^{11}+3\zeta_{6}q^{13}+\cdots$
1008.3.f.g	$1008$	$3$	1008.f	7.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$0$	$0$	$-8$	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+2\beta _{2})q^{5}+(-2-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1008.3.f.h	$1008$	$3$	1008.f	7.b	$2$	$4$	$4$	$27.466$	4.0.2048.2	None		$2$	$0$	$0$	$0$	$0$	$-4$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{7}+\cdots$
1008.3.f.i	$1008$	$3$	1008.f	7.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{2}, \sqrt{-33})$	None		$4$	$0$	$0$	$0$	$0$	$16$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(4+\beta _{3})q^{7}+3\beta _{2}q^{11}+4\beta _{3}q^{13}+\cdots$
1008.3.f.j	$1008$	$3$	1008.f	7.b	$2$	$8$	$8$	$27.466$	8.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$0$	$4$	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{5}+(1-\beta _{3}+\beta _{4})q^{7}+(-3-2\beta _{1}+\cdots)q^{11}+\cdots$
1008.3.f.k	$1008$	$3$	1008.f	7.b	$2$	$8$	$8$	$27.466$	8.0.$\cdots$.3	None		$4$	$0$	$0$	$0$	$0$	$4$	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{5}+(1+\beta _{3})q^{7}+\beta _{5}q^{11}+(-1+\cdots)q^{13}+\cdots$
1008.3.m.a	$1008$	$3$	1008.m	4.b	$2$	$2$	$2$	$27.466$	$\Q(\sqrt{-7}) $	None		$2$	$0$	$0$	$0$	$-16$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q-8q^{5}-\beta q^{7}-4\beta q^{11}-4q^{13}+2q^{17}+\cdots$
1008.3.m.b	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$2$	$0$	$0$	$0$	$-4$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-\beta _{2}+\beta _{3})q^{11}+\cdots$
1008.3.m.c	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	$\Q(i, \sqrt{7})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+2q^{13}+\cdots$
1008.3.m.d	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$2$	$0$	$0$	$0$	$4$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-2\beta _{2}+2\beta _{3})q^{11}+\cdots$
1008.3.m.e	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$2$	$0$	$0$	$0$	$8$	$0$	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{5}-\beta _{1}q^{7}+(4\beta _{1}+\beta _{3})q^{11}+(2+\cdots)q^{13}+\cdots$
1008.3.m.f	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$2$	$0$	$0$	$0$	$20$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(5-\beta _{1})q^{5}+\beta _{3}q^{7}+(3\beta _{2}+5\beta _{3})q^{11}+\cdots$
1008.3.m.g	$1008$	$3$	1008.m	4.b	$2$	$8$	$8$	$27.466$	8.0.49787136.1	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}-\beta _{1}q^{7}-\beta _{2}q^{11}-10q^{13}+\cdots$
1008.3.o.a	$1008$	$3$	1008.o	84.h	$2$	$8$	$8$	$27.466$	8.0.$\cdots$.5	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{4}q^{7}-\beta _{2}q^{11}+\beta _{5}q^{13}+\cdots$
1008.3.o.b	$1008$	$3$	1008.o	84.h	$2$	$24$	$24$	$27.466$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1008.3.bk.a	$1008$	$3$	1008.bk	84.j	$6$	$20$	$10$	$27.466$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$-10$	$2^{12}\cdot 3^{13}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{5}-\beta _{9}q^{7}+(\beta _{1}-\beta _{17}+\beta _{18}+\cdots)q^{11}+\cdots$
1008.3.bk.b	$1008$	$3$	1008.bk	84.j	$6$	$20$	$10$	$27.466$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$10$	$2^{12}\cdot 3^{13}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{5}+\beta _{9}q^{7}+(-\beta _{1}+\beta _{17}-\beta _{18}+\cdots)q^{11}+\cdots$
1008.3.bk.c	$1008$	$3$	1008.bk	84.j	$6$	$24$	$12$	$27.466$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
1008.3.cd.a	$1008$	$3$	1008.cd	28.g	$6$	$2$	$1$	$27.466$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-13$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-5-3\zeta_{6})q^{7}-23q^{13}+(21+21\zeta_{6})q^{19}+\cdots$
1008.3.cd.b	$1008$	$3$	1008.cd	28.g	$6$	$2$	$1$	$27.466$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-11$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-3-5\zeta_{6})q^{7}+q^{13}+(-5-5\zeta_{6})q^{19}+\cdots$
1008.3.cd.c	$1008$	$3$	1008.cd	28.g	$6$	$2$	$1$	$27.466$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$11$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3+5\zeta_{6})q^{7}+q^{13}+(5+5\zeta_{6})q^{19}+\cdots$
1008.3.cd.d	$1008$	$3$	1008.cd	28.g	$6$	$2$	$1$	$27.466$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$13$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(5+3\zeta_{6})q^{7}-23q^{13}+(-21-21\zeta_{6})q^{19}+\cdots$
1008.3.cd.e	$1008$	$3$	1008.cd	28.g	$6$	$4$	$2$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		$4$	$0$	$0$	$0$	$-2$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{5}+(3\beta _{1}-\beta _{3})q^{7}-5\beta _{1}q^{11}+\cdots$
1008.3.cd.f	$1008$	$3$	1008.cd	28.g	$6$	$4$	$2$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$0$	$0$	$-1$	$-12$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\beta _{1}-\beta _{3})q^{5}+(-3-3\beta _{1}+\cdots)q^{7}+\cdots$
1008.3.cd.g	$1008$	$3$	1008.cd	28.g	$6$	$4$	$2$	$27.466$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		$2$	$0$	$0$	$0$	$-1$	$12$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\beta _{1}-\beta _{3})q^{5}+(3+3\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
1008.3.cd.h	$1008$	$3$	1008.cd	28.g	$6$	$6$	$3$	$27.466$	6.0.1364138928.1	None		$2$	$0$	$0$	$0$	$-1$	$-11$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{5}+(-3+\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
1008.3.cd.i	$1008$	$3$	1008.cd	28.g	$6$	$6$	$3$	$27.466$	6.0.1364138928.1	None		$2$	$0$	$0$	$0$	$-1$	$11$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{5}+(2-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots$
1008.3.cd.j	$1008$	$3$	1008.cd	28.g	$6$	$6$	$3$	$27.466$	6.0.259470000.1	None		$2$	$0$	$0$	$0$	$1$	$-14$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{5}+(-4-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
1008.3.cd.k	$1008$	$3$	1008.cd	28.g	$6$	$6$	$3$	$27.466$	6.0.259470000.1	None		$2$	$0$	$0$	$0$	$1$	$14$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{5}+(4+\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
1008.3.cd.l	$1008$	$3$	1008.cd	28.g	$6$	$6$	$3$	$27.466$	6.0.2682209403.3	None		$2$	$0$	$0$	$0$	$2$	$-11$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
1008.3.cd.m	$1008$	$3$	1008.cd	28.g	$6$	$6$	$3$	$27.466$	6.0.2682209403.3	None		$2$	$0$	$0$	$0$	$2$	$11$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(2-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1008.3.cd.n	$1008$	$3$	1008.cd	28.g	$6$	$8$	$4$	$27.466$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$-24$	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{5}+(-1-5\beta _{1}+\beta _{3}+3\beta _{4}+\cdots)q^{7}+\cdots$
1008.3.cd.o	$1008$	$3$	1008.cd	28.g	$6$	$8$	$4$	$27.466$	8.0.$\cdots$.8	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{5}+(2\beta _{3}+\beta _{4})q^{7}-\beta _{6}q^{11}+\cdots$
1008.3.cd.p	$1008$	$3$	1008.cd	28.g	$6$	$8$	$4$	$27.466$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$24$	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{5}+(1+5\beta _{1}-\beta _{3}-3\beta _{4})q^{7}+\cdots$
1008.3.cg.a	$1008$	$3$	1008.cg	7.d	$6$	$2$	$1$	$27.466$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-9$	$-13$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-6+3\zeta_{6})q^{5}+(-5-3\zeta_{6})q^{7}+\cdots$

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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.