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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
19.2.e.a	$19$	$2$	19.e	19.e	$9$	$6$	$1$	$0.152$	$\Q(\zeta_{18})$	None		$2$	$0$	$-6$	$-3$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots$
23.2.c.a	$23$	$2$	23.c	23.c	$11$	$10$	$1$	$0.184$	$\Q(\zeta_{22})$	None		$2$	$0$	$-7$	$-7$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
25.2.e.a	$25$	$2$	25.e	25.e	$10$	$8$	$2$	$0.200$	8.0.58140625.2	None		$2$	$0$	$-5$	$-5$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots$
29.2.d.a	$29$	$2$	29.d	29.d	$7$	$6$	$1$	$0.232$	$\Q(\zeta_{14})$	None		$2$	$0$	$-2$	$-5$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
32.2.g.b	$32$	$2$	32.g	32.g	$8$	$8$	$2$	$0.256$	8.0.18939904.2	None		$2$	$0$	$-4$	$-4$	$0$	$-8$	$2$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots$
33.2.f.a	$33$	$2$	33.f	33.f	$10$	$8$	$2$	$0.264$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$-6$	$0$	$-10$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots$
36.2.h.a	$36$	$2$	36.h	36.h	$6$	$8$	$4$	$0.287$	8.0.170772624.1	None		$4$	$0$	$-3$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
37.2.f.a	$37$	$2$	37.f	37.f	$9$	$6$	$1$	$0.295$	$\Q(\zeta_{18})$	None		$2$	$0$	$-6$	$3$	$-6$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}^{5})q^{2}+(\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
37.2.f.b	$37$	$2$	37.f	37.f	$9$	$6$	$1$	$0.295$	$\Q(\zeta_{18})$	None		$2$	$0$	$3$	$-6$	$6$	$-12$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots$
38.2.e.a	$38$	$2$	38.e	19.e	$9$	$6$	$1$	$0.303$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$-3$	$0$	$-6$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\zeta_{18}q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{2}q^{4}+\cdots$
39.2.k.b	$39$	$2$	39.k	39.k	$12$	$8$	$2$	$0.311$	8.0.56070144.2	None		$4$	$0$	$0$	$-2$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+2\beta _{5}+\beta _{7})q^{2}+\cdots$
40.2.k.a	$40$	$2$	40.k	40.k	$4$	$8$	$4$	$0.319$	$\Q(\zeta_{20})$	None		$4$	$0$	$-2$	$-4$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots$
41.2.c.a	$41$	$2$	41.c	41.c	$4$	$6$	$3$	$0.327$	6.0.5089536.1	None		$2$	$0$	$0$	$-4$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{5}q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$
41.2.d.a	$41$	$2$	41.d	41.d	$5$	$8$	$2$	$0.327$	8.0.13140625.1	None		$2$	$0$	$-1$	$-6$	$3$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}-\beta _{7})q^{2}+(-1+\beta _{5})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
41.2.f.a	$41$	$2$	41.f	41.f	$10$	$8$	$2$	$0.327$	$\Q(\zeta_{15})$	None		$2$	$0$	$-3$	$0$	$-9$	$-5$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1-\zeta_{15}-\zeta_{15}^{5}-\zeta_{15}^{6})q^{2}+\cdots$
43.2.e.a	$43$	$2$	43.e	43.e	$7$	$6$	$1$	$0.343$	$\Q(\zeta_{14})$	None		$2$	$0$	$-5$	$2$	$-3$	$0$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots$
43.2.e.b	$43$	$2$	43.e	43.e	$7$	$6$	$1$	$0.343$	$\Q(\zeta_{14})$	None		$2$	$0$	$3$	$-3$	$2$	$-16$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\zeta_{14}+\zeta_{14}^{3}+\zeta_{14}^{5})q^{2}+(-1+\zeta_{14}+\cdots)q^{3}+\cdots$
45.2.e.b	$45$	$2$	45.e	9.c	$3$	$6$	$3$	$0.359$	6.0.954288.1	None		$2$	$0$	$-1$	$1$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots$
45.2.j.a	$45$	$2$	45.j	45.j	$6$	$8$	$4$	$0.359$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{6}q^{2}+(\zeta_{24}^{5}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{3}q^{4}+\cdots$
46.2.c.a	$46$	$2$	46.c	23.c	$11$	$10$	$1$	$0.367$	$\Q(\zeta_{22})$	None		$2$	$0$	$-1$	$-4$	$-6$	$3$	$1$	$\mathrm{SU}(2)[C_{11}]$	$q-\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{7}+\cdots)q^{3}+\cdots$
46.2.c.b	$46$	$2$	46.c	23.c	$11$	$10$	$1$	$0.367$	$\Q(\zeta_{22})$	None		$2$	$0$	$1$	$0$	$-4$	$-7$	$1$	$\mathrm{SU}(2)[C_{11}]$	$q+\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\zeta_{22}^{7}+\cdots)q^{3}+\cdots$
48.2.j.a	$48$	$2$	48.j	16.e	$4$	$8$	$4$	$0.383$	8.0.18939904.2	None		$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{5}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
49.2.e.a	$49$	$2$	49.e	49.e	$7$	$6$	$1$	$0.391$	$\Q(\zeta_{14})$	None		$2$	$0$	$-3$	$-3$	$6$	$7$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
50.2.d.b	$50$	$2$	50.d	25.d	$5$	$8$	$2$	$0.399$	8.0.58140625.2	None		$2$	$0$	$-2$	$-3$	$0$	$4$	$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+\cdots$
50.2.e.a	$50$	$2$	50.e	25.e	$10$	$8$	$2$	$0.399$	$\Q(\zeta_{20})$	None		$2$	$0$	$0$	$0$	$-10$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+(-1+\zeta_{20}^{2}-\zeta_{20}^{4}+2\zeta_{20}^{6}+\cdots)q^{3}+\cdots$
51.2.e.a	$51$	$2$	51.e	17.c	$4$	$8$	$4$	$0.407$	8.0.836829184.2	None		$2$	$0$	$0$	$0$	$-4$	$-4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
51.2.h.a	$51$	$2$	51.h	17.d	$8$	$8$	$2$	$0.407$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$-8$	$0$	$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
52.2.f.b	$52$	$2$	52.f	52.f	$4$	$8$	$4$	$0.415$	8.0.18939904.2	None		$4$	$0$	$-4$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2}-\beta _{5}+\beta _{7})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots$
54.2.e.a	$54$	$2$	54.e	27.e	$9$	$6$	$1$	$0.431$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$0$	$-3$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+\cdots$
16.3.f.a	$16$	$3$	16.f	16.f	$4$	$6$	$3$	$0.436$	6.0.399424.1	None		$2$	$0$	$-2$	$-2$	$-2$	$-4$	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
55.2.g.a	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.159390625.1	None		$2$	$0$	$-4$	$1$	$-2$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots$
55.2.g.b	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.13140625.1	None		$2$	$0$	$-2$	$-5$	$2$	$-1$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
57.2.e.b	$57$	$2$	57.e	19.c	$3$	$6$	$3$	$0.455$	6.0.954288.1	None		$2$	$0$	$1$	$-3$	$-2$	$-2$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots$
57.2.f.a	$57$	$2$	57.f	57.f	$6$	$8$	$4$	$0.455$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$0$	$0$	$-16$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(\zeta_{24}^{2}+\cdots)q^{3}+\cdots$
57.2.i.a	$57$	$2$	57.i	19.e	$9$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	None		$2$	$0$	$3$	$0$	$-6$	$3$	$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots$
57.2.j.a	$57$	$2$	57.j	57.j	$18$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{18}]$	$q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots$
58.2.d.a	$58$	$2$	58.d	29.d	$7$	$6$	$1$	$0.463$	$\Q(\zeta_{14})$	None		$2$	$0$	$1$	$3$	$-4$	$-5$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+\cdots$
17.3.e.a	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	$\Q(\zeta_{16})$	None		$2$	$0$	$-8$	$-8$	$16$	$8$	$1$	$\mathrm{SU}(2)[C_{16}]$	$q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots$
17.3.e.b	$17$	$3$	17.e	17.e	$16$	$8$	$1$	$0.463$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$-24$	$-16$	$1$	$\mathrm{SU}(2)[C_{16}]$	$q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots$
60.2.e.a	$60$	$2$	60.e	12.b	$2$	$8$	$8$	$0.479$	8.0.342102016.5	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{4}-\beta _{7})q^{3}+(\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
61.2.c.a	$61$	$2$	61.c	61.c	$3$	$8$	$4$	$0.487$	8.0.310217769.2	None		$2$	$0$	$0$	$-6$	$-2$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
61.2.f.b	$61$	$2$	61.f	61.f	$6$	$8$	$4$	$0.487$	8.0.542936601.2	None		$2$	$0$	$0$	$-2$	$6$	$-3$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{6})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots$
62.2.d.a	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.511890625.1	None		$2$	$0$	$-2$	$-4$	$-4$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$
62.2.d.b	$62$	$2$	62.d	31.d	$5$	$8$	$2$	$0.495$	8.0.1903140625.1	None		$2$	$0$	$2$	$-2$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
62.2.g.a	$62$	$2$	62.g	31.g	$15$	$8$	$1$	$0.495$	$\Q(\zeta_{15})$	None		$2$	$0$	$-2$	$3$	$1$	$2$	$1$	$\mathrm{SU}(2)[C_{15}]$	$q+\zeta_{15}^{6}q^{2}+(\zeta_{15}+\zeta_{15}^{4}+\zeta_{15}^{7})q^{3}+\cdots$
62.2.g.b	$62$	$2$	62.g	31.g	$15$	$8$	$1$	$0.495$	$\Q(\zeta_{15})$	None		$2$	$0$	$2$	$1$	$-3$	$-16$	$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\zeta_{15}^{6}q^{2}+(\zeta_{15}-\zeta_{15}^{4}+\zeta_{15}^{7})q^{3}+\cdots$
63.2.f.a	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	$\Q(\zeta_{18})$	None		$2$	$0$	$-3$	$0$	$-3$	$-3$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
63.2.f.b	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	6.0.309123.1	None		$2$	$0$	$1$	$-4$	$5$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$
63.2.g.b	$63$	$2$	63.g	63.g	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	None		$2$	$0$	$2$	$2$	$-8$	$-1$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
63.2.h.b	$63$	$2$	63.h	63.h	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	None		$2$	$0$	$-4$	$-1$	$4$	$-4$	$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$

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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.