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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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1936.1.d.a	$1936$	$1$	1936.d	4.b	$2$	$1$	$1$	$0.966$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{11}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}+q^{9}+3q^{25}+2q^{37}-2q^{45}+\cdots$
1936.1.d.b	$1936$	$1$	1936.d	4.b	$2$	$2$	$2$	$0.966$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{5}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
1936.1.d.c	$1936$	$1$	1936.d	4.b	$2$	$2$	$2$	$0.966$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}+q^{9}-\beta q^{13}+\beta q^{17}+\beta q^{29}+\cdots$
1936.1.h.a	$1936$	$1$	1936.h	11.b	$2$	$2$	$2$	$0.966$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$2$	$2$	$0$		$1$		$q+q^{3}+q^{5}-\beta q^{7}+q^{15}+\beta q^{17}+\cdots$
1936.1.n.a	$1936$	$1$	1936.n	11.d	$10$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-\zeta_{10}^{3}q^{3}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{15}+\cdots$
1936.1.n.b	$1936$	$1$	1936.n	11.d	$10$	$8$	$2$	$0.966$	8.0.64000000.1	$S_{4}$	None	None		$8$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q-\beta _{6}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{6})q^{5}+\cdots$
1936.1.r.a	$1936$	$1$	1936.r	44.h	$10$	$4$	$1$	$0.966$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{11}) $		$16$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+3\zeta_{10}^{4}q^{25}+\cdots$
1936.1.r.b	$1936$	$1$	1936.r	44.h	$10$	$8$	$2$	$0.966$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-1}) $	None		$16$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{5}+\beta _{2}q^{9}+\cdots$
1936.1.r.c	$1936$	$1$	1936.r	44.h	$10$	$8$	$2$	$0.966$	$\Q(\zeta_{15})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$16$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$		$q+(\zeta_{30}^{2}+\zeta_{30}^{7})q^{3}+\zeta_{30}^{6}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots$
1936.2.a.a	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}-2q^{15}+\cdots$
1936.2.a.b	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}+q^{13}-2q^{15}+\cdots$
1936.2.a.c	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+2q^{7}-2q^{9}+4q^{13}+\cdots$
1936.2.a.d	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}-2q^{9}+4q^{13}+\cdots$
1936.2.a.e	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}-2q^{9}-4q^{13}+\cdots$
1936.2.a.f	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}-3q^{9}+3q^{13}+3q^{17}+\cdots$
1936.2.a.g	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-3q^{9}-3q^{13}-3q^{17}+\cdots$
1936.2.a.h	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$-3$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q+q^{3}-3q^{5}-2q^{9}-3q^{15}+9q^{23}+\cdots$
1936.2.a.i	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{13}+\cdots$
1936.2.a.j	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}-2q^{7}+q^{9}+5q^{13}+\cdots$
1936.2.a.k	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}+2q^{7}+q^{9}-5q^{13}+\cdots$
1936.2.a.l	$1936$	$2$	1936.a	1.a	$1$	$1$	$1$	$15.459$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}-2q^{7}+6q^{9}-9q^{15}+\cdots$
1936.2.a.m	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$-4$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{5}+2\beta q^{7}+q^{9}+3\beta q^{13}+\cdots$
1936.2.a.n	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(2-2\beta )q^{5}-2q^{7}+\cdots$
1936.2.a.o	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(2-2\beta )q^{5}+2q^{7}+\cdots$
1936.2.a.p	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-2+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
1936.2.a.q	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-2+\beta )q^{5}+(1-\beta )q^{7}+\cdots$
1936.2.a.r	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots$
1936.2.a.s	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{33}) $	$_{}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$3$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-\beta q^{3}+(2-\beta )q^{5}+(5+\beta )q^{9}+(8-\beta )q^{15}+\cdots$
1936.2.a.t	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}-\beta q^{7}+(-2+\cdots)q^{9}+\cdots$
1936.2.a.u	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(-2+\cdots)q^{9}+\cdots$
1936.2.a.v	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+(-3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1936.2.a.w	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
1936.2.a.x	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+(1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
1936.2.a.y	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
1936.2.a.z	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+(1-3\beta )q^{7}+(-1+\cdots)q^{9}+\cdots$
1936.2.a.ba	$1936$	$2$	1936.a	1.a	$1$	$2$	$2$	$15.459$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}+(-1+3\beta )q^{7}+\cdots$
1936.2.a.bb	$1936$	$2$	1936.a	1.a	$1$	$4$	$4$	$15.459$	4.4.5225.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
1936.2.a.bc	$1936$	$2$	1936.a	1.a	$1$	$4$	$4$	$15.459$	4.4.5225.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
1936.2.e.a	$1936$	$2$	1936.e	44.c	$2$	$2$	$2$	$15.459$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{5}+3q^{9}+5\beta q^{13}-3\beta q^{17}+\cdots$
1936.2.e.b	$1936$	$2$	1936.e	44.c	$2$	$4$	$4$	$15.459$	$\Q(\sqrt{-2}, \sqrt{-7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-3q^{5}-\beta _{1}q^{7}-4q^{9}-2\beta _{2}q^{13}+\cdots$
1936.2.e.c	$1936$	$2$	1936.e	44.c	$2$	$4$	$4$	$15.459$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-8$	$0$		$11$	$\mathrm{U}(1)[D_{2}]$	$q+(-2+\beta _{1})q^{5}+3q^{9}+\beta _{2}q^{13}+(-\beta _{2}+\cdots)q^{17}+\cdots$
1936.2.e.d	$1936$	$2$	1936.e	44.c	$2$	$4$	$4$	$15.459$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+q^{5}-\beta _{3}q^{7}+4\beta _{1}q^{13}+\cdots$
1936.2.e.e	$1936$	$2$	1936.e	44.c	$2$	$8$	$8$	$15.459$	8.0.484000000.6	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
1936.2.e.f	$1936$	$2$	1936.e	44.c	$2$	$16$	$16$	$15.459$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{4}-\beta _{13})q^{3}+(\beta _{5}+\beta _{12})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1936.2.e.g	$1936$	$2$	1936.e	44.c	$2$	$16$	$16$	$15.459$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$		$2^{12}\cdot 3^{2}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-\beta _{11}q^{7}+\cdots$
1936.4.a.a	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	$\Q$	$_{}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$1$	$0$	$-8$	$18$	$0$	$-$	$1$	$N(\mathrm{U}(1))$	$q-8q^{3}+18q^{5}+37q^{9}-12^{2}q^{15}+\cdots$
1936.4.a.b	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-7$	$9$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-7q^{3}+9q^{5}+2q^{7}+22q^{9}-63q^{15}+\cdots$
1936.4.a.c	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-5$	$-15$	$-36$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{3}-15q^{5}-6^{2}q^{7}-2q^{9}-12q^{13}+\cdots$
1936.4.a.d	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-5$	$-15$	$36$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{3}-15q^{5}+6^{2}q^{7}-2q^{9}+12q^{13}+\cdots$
1936.4.a.e	$1936$	$4$	1936.a	1.a	$1$	$1$	$1$	$114.228$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-4$	$3$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{3}+3q^{5}-8q^{7}-11q^{9}+83q^{13}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 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.