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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
639.1.g.b	$639$	$1$	639.g	639.g	$6$	$12$	$6$	$0.319$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-1$	$1$	$2$	$0$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots$
56.2.m.a	$56$	$2$	56.m	56.m	$6$	$12$	$6$	$0.447$	12.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{8})q^{2}+(-1-\beta _{10})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
56.2.p.a	$56$	$2$	56.p	56.p	$6$	$12$	$6$	$0.447$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$-4$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{6}q^{3}-\beta _{3}q^{4}+\cdots$
63.2.o.a	$63$	$2$	63.o	63.o	$6$	$12$	$6$	$0.503$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$-6$	$0$	$0$	$-2$	$3$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+\cdots$
65.2.n.a	$65$	$2$	65.n	65.n	$6$	$12$	$6$	$0.519$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}+(\beta _{4}-\beta _{11})q^{3}+(-\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots$
72.2.l.b	$72$	$2$	72.l	72.l	$6$	$16$	$8$	$0.575$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$-3$	$-6$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots$
72.2.n.b	$72$	$2$	72.n	72.n	$6$	$16$	$8$	$0.575$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$1$	$0$	$0$	$6$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots$
1169.1.f.c	$1169$	$1$	1169.f	1169.f	$6$	$20$	$10$	$0.583$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$2$	$-1$	$0$	$1$	$1$		$q+(\zeta_{66}^{16}+\zeta_{66}^{28})q^{2}+(-\zeta_{66}^{9}-\zeta_{66}^{13}+\cdots)q^{3}+\cdots$
1176.1.be.a	$1176$	$1$	1176.be	168.ae	$6$	$16$	$8$	$0.587$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots$
1183.1.t.a	$1183$	$1$	1183.t	91.t	$6$	$12$	$6$	$0.590$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
76.2.f.a	$76$	$2$	76.f	76.f	$6$	$16$	$8$	$0.607$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$-3$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots$
77.2.i.a	$77$	$2$	77.i	77.i	$6$	$12$	$6$	$0.615$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{7})q^{2}+(-1+\beta _{2}-\beta _{8}-\beta _{9}+\cdots)q^{3}+\cdots$
1235.1.bm.a	$1235$	$1$	1235.bm	1235.am	$6$	$16$	$8$	$0.616$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{48}^{13}+\zeta_{48}^{19})q^{2}+(-\zeta_{48}^{15}+\cdots)q^{3}+\cdots$
1349.1.g.b	$1349$	$1$	1349.g	1349.g	$6$	$12$	$6$	$0.673$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{42}^{8}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{3}+\zeta_{42}^{4}+\cdots)q^{3}+\cdots$
1352.1.p.c	$1352$	$1$	1352.p	104.p	$6$	$12$	$6$	$0.675$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+\beta _{11}q^{6}+\cdots$
85.2.l.a	$85$	$2$	85.l	17.d	$8$	$24$	$6$	$0.679$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
85.2.m.a	$85$	$2$	85.m	85.m	$8$	$24$	$6$	$0.679$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
1372.1.g.a	$1372$	$1$	1372.g	28.g	$6$	$12$	$6$	$0.685$	$\Q(\zeta_{21})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{42}^{5}q^{2}+\zeta_{42}^{10}q^{4}+\zeta_{42}^{15}q^{8}+\cdots$
1393.1.n.a	$1393$	$1$	1393.n	1393.n	$6$	$18$	$9$	$0.695$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-199}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(\zeta_{54}^{10}+\zeta_{54}^{18}+\cdots)q^{4}+\cdots$
88.2.k.b	$88$	$2$	88.k	88.k	$10$	$32$	$8$	$0.703$		$_{}$	None	None		$4$	$0$	$-5$	$-2$	$0$	$0$		$\mathrm{SU}(2)[C_{10}]$
88.2.o.a	$88$	$2$	88.o	88.o	$10$	$40$	$10$	$0.703$		$_{}$	None	None		$4$	$0$	$-5$	$0$	$0$	$-10$		$\mathrm{SU}(2)[C_{10}]$
91.2.k.b	$91$	$2$	91.k	91.k	$6$	$12$	$6$	$0.727$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-3$	$-3$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{9}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots$
91.2.q.a	$91$	$2$	91.q	13.e	$6$	$12$	$6$	$0.727$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{4}-\beta _{6}+\beta _{10})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots$
91.2.r.a	$91$	$2$	91.r	91.r	$6$	$16$	$8$	$0.727$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{11}q^{2}+(-1+\beta _{3}+\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots$
91.2.u.b	$91$	$2$	91.u	91.u	$6$	$12$	$6$	$0.727$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$3$	$3$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots$
93.2.k.a	$93$	$2$	93.k	93.k	$10$	$32$	$8$	$0.743$		$_{}$	None	None		$4$	$0$	$0$	$-5$	$0$	$8$		$\mathrm{SU}(2)[C_{10}]$
1503.1.f.b	$1503$	$1$	1503.f	1503.f	$6$	$20$	$10$	$0.750$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q+(-\zeta_{66}^{9}-\zeta_{66}^{13})q^{2}+\zeta_{66}^{14}q^{3}+\cdots$
1505.1.x.c	$1505$	$1$	1505.x	1505.x	$6$	$12$	$6$	$0.751$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$-1$	$2$	$-6$	$1$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}+(-\zeta_{42}-\zeta_{42}^{13}+\cdots)q^{3}+\cdots$
1505.1.x.d	$1505$	$1$	1505.x	1505.x	$6$	$12$	$6$	$0.751$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$1$	$-2$	$6$	$-1$	$1$		$q+(\zeta_{42}^{3}-\zeta_{42}^{4})q^{2}+(\zeta_{42}+\zeta_{42}^{13}+\cdots)q^{3}+\cdots$
1508.1.v.c	$1508$	$1$	1508.v	1508.v	$6$	$12$	$6$	$0.753$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{36}^{15}q^{2}+(\zeta_{36}^{5}+\zeta_{36}^{7})q^{3}-\zeta_{36}^{12}q^{4}+\cdots$
95.2.i.b	$95$	$2$	95.i	95.i	$6$	$12$	$6$	$0.759$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
28.3.g.a	$28$	$3$	28.g	28.g	$6$	$12$	$6$	$0.763$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$-2$	$0$	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{5}+\beta _{9}+\cdots)q^{4}+\cdots$
96.2.n.a	$96$	$2$	96.n	32.g	$8$	$32$	$8$	$0.767$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
97.2.e.a	$97$	$2$	97.e	97.e	$6$	$14$	$7$	$0.775$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$-2$	$6$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+(-\beta _{1}-\beta _{7}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots$
97.2.f.a	$97$	$2$	97.f	97.f	$8$	$24$	$6$	$0.775$		$_{}$	None	None		$2$	$0$	$-4$	$-8$	$4$	$8$		$\mathrm{SU}(2)[C_{8}]$
1561.1.n.c	$1561$	$1$	1561.n	1561.n	$6$	$12$	$6$	$0.779$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-223}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}+(\zeta_{42}^{6}-\zeta_{42}^{7}+\cdots)q^{4}+\cdots$
99.2.g.b	$99$	$2$	99.g	99.g	$6$	$16$	$8$	$0.791$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(\beta _{6}-\beta _{7}+\beta _{9}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots$
101.2.e.b	$101$	$2$	101.e	101.e	$10$	$28$	$7$	$0.806$		$_{}$	None	None		$2$	$0$	$0$	$0$	$1$	$5$		$\mathrm{SU}(2)[C_{10}]$
1617.1.k.e	$1617$	$1$	1617.k	231.k	$6$	$16$	$8$	$0.807$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+(\zeta_{48}-\zeta_{48}^{7}+\cdots)q^{5}+\cdots$
1661.1.t.b	$1661$	$1$	1661.t	1661.t	$10$	$24$	$6$	$0.829$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-3$	$0$	$2$	$0$	$1$		$q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{2}-\zeta_{70}^{5}+\cdots)q^{4}+\cdots$
104.2.s.c	$104$	$2$	104.s	104.s	$6$	$16$	$8$	$0.830$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$3$	$0$	$0$	$18$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{3}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
105.2.q.a	$105$	$2$	105.q	35.j	$6$	$16$	$8$	$0.838$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{5}+\beta _{6}-\beta _{15})q^{2}+\beta _{3}q^{3}+(1+\cdots)q^{4}+\cdots$
109.2.e.b	$109$	$2$	109.e	109.e	$6$	$14$	$7$	$0.870$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-2$	$-7$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(\beta _{5}+\beta _{10}-\beta _{13})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
109.2.f.a	$109$	$2$	109.f	109.f	$9$	$42$	$7$	$0.870$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$-6$	$3$		$\mathrm{SU}(2)[C_{9}]$
32.3.h.a	$32$	$3$	32.h	32.h	$8$	$28$	$7$	$0.872$		$_{}$	None	None		$2$	$0$	$-4$	$-4$	$-4$	$-4$		$\mathrm{SU}(2)[C_{8}]$
1757.1.h.b	$1757$	$1$	1757.h	1757.h	$6$	$12$	$6$	$0.877$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-251}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-2$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{3}+\zeta_{42}^{14}q^{4}+\cdots$
1764.1.q.b	$1764$	$1$	1764.q	84.j	$6$	$16$	$8$	$0.880$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$2^{6}$		$q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots$
1775.1.p.b	$1775$	$1$	1775.p	1775.p	$10$	$24$	$6$	$0.886$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-3$	$2$	$1$	$0$	$1$		$q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{18}+\zeta_{70}^{24}+\cdots)q^{3}+\cdots$
1775.1.bb.b	$1775$	$1$	1775.bb	1775.ab	$10$	$24$	$6$	$0.886$	$\Q(\zeta_{35})$	$D_{70}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-5$	$0$	$-1$	$0$	$1$		$q+(\zeta_{70}^{17}-\zeta_{70}^{25})q^{2}+(-\zeta_{70}^{23}+\cdots)q^{3}+\cdots$
113.2.d.a	$113$	$2$	113.d	113.d	$7$	$48$	$8$	$0.902$		$_{}$	None	None		$2$	$0$	$-8$	$-1$	$1$	$-3$		$\mathrm{SU}(2)[C_{7}]$

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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.