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Label	Degree	Type	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
648.557.1a	$1$	R	$1$	$\Q$	648.557.1a	$S_4\times \He_3$	$C_1$	$1$	1.a1	$648$	1.a1	$648$	$1$	$1$
648.557.1b	$1$	R	$1$	$\Q$	648.557.1b	$S_4\times \He_3$	$C_2$	$2$	2.a1	$324$	1.a1	$648$	$1$	$1$
648.557.1c1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1c	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1c2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1c	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1d1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1d	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1d2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1d	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1e1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1e	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1e2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1e	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1f1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1f	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1f2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1f	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1g1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1g	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1g2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1g	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1h1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1h	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1h2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1h	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1i1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1i	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1i2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1i	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1j1	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1j	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1j2	$1$	C	$3$	$\Q(\sqrt{-3}) $	648.557.1j	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.2a	$2$	R	$1$	$\Q$	648.557.2a	$S_4\times \He_3$	$S_3$	$6$	6.b1	$108$	6.b1	$108$	$6$	$1$
648.557.2b1	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2b	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2b2	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2b	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2c1	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2c	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2c2	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2c	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2d1	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2d	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2d2	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2d	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2e1	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2e	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2e2	$2$	C	$3$	$\Q(\sqrt{-3}) $	648.557.2e	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.3a	$3$	R	$1$	$\Q$	648.557.3a	$S_4\times \He_3$	$S_4$	$24$	24.a1	$27$	24.a1	$27$	$24$	$1$
648.557.3b	$3$	R	$1$	$\Q$	648.557.3b	$S_4\times \He_3$	$S_4$	$24$	24.a1	$27$	24.a1	$27$	$24$	$1$
648.557.3c1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3c	$S_4\times \He_3$	$\He_3$	$27$	27.a1	$24$	9.a1	$72$	$9$	$1$
648.557.3c2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3c	$S_4\times \He_3$	$\He_3$	$27$	27.a1	$24$	9.a1	$72$	$9$	$1$
648.557.3d1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3d	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3d2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3d	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3e1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3e	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3e2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3e	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3f1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3f	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3f2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3f	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3g1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3g	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3g2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3g	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3h1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3h	$S_4\times \He_3$	$C_2\times \He_3$	$54$	54.b1	$12$	9.a1	$72$	$9$	$1$
648.557.3h2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3h	$S_4\times \He_3$	$C_2\times \He_3$	$54$	54.b1	$12$	9.a1	$72$	$9$	$1$
648.557.3i1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3i	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3i2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3i	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3j1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3j	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3j2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3j	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3k1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3k	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3k2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3k	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3l1	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3l	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3l2	$3$	C	$3$	$\Q(\sqrt{-3}) $	648.557.3l	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.6a1	$6$	C	$3$	$\Q(\sqrt{-3}) $	648.557.6a	$S_4\times \He_3$	$S_3\times \He_3$	$162$	162.a1	$4$	54.a1	$12$	$54$	$1$

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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.

Label	Degree	Type	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
648.557.1a	$1$	R	$1$	\(\Q\)	648.557.1a	$S_4\times \He_3$	$C_1$	$1$	1.a1	$648$	1.a1	$648$	$1$	$1$
648.557.1b	$1$	R	$1$	\(\Q\)	648.557.1b	$S_4\times \He_3$	$C_2$	$2$	2.a1	$324$	1.a1	$648$	$1$	$1$
648.557.1c1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1c	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1c2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1c	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1d1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1d	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1d2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1d	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1e1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1e	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1e2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1e	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1f1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1f	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1f2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1f	$S_4\times \He_3$	$C_3$	$3$	3.a1	$216$	1.a1	$648$	$1$	$1$
648.557.1g1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1g	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1g2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1g	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1h1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1h	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1h2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1h	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1i1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1i	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1i2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1i	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1j1	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1j	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.1j2	$1$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.1j	$S_4\times \He_3$	$C_6$	$6$	6.a1	$108$	1.a1	$648$	$1$	$1$
648.557.2a	$2$	R	$1$	\(\Q\)	648.557.2a	$S_4\times \He_3$	$S_3$	$6$	6.b1	$108$	6.b1	$108$	$6$	$1$
648.557.2b1	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2b	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2b2	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2b	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2c1	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2c	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2c2	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2c	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2d1	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2d	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2d2	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2d	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2e1	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2e	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.2e2	$2$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.2e	$S_4\times \He_3$	$C_3\times S_3$	$18$	18.a1	$36$	6.b1	$108$	$6$	$1$
648.557.3a	$3$	R	$1$	\(\Q\)	648.557.3a	$S_4\times \He_3$	$S_4$	$24$	24.a1	$27$	24.a1	$27$	$24$	$1$
648.557.3b	$3$	R	$1$	\(\Q\)	648.557.3b	$S_4\times \He_3$	$S_4$	$24$	24.a1	$27$	24.a1	$27$	$24$	$1$
648.557.3c1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3c	$S_4\times \He_3$	$\He_3$	$27$	27.a1	$24$	9.a1	$72$	$9$	$1$
648.557.3c2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3c	$S_4\times \He_3$	$\He_3$	$27$	27.a1	$24$	9.a1	$72$	$9$	$1$
648.557.3d1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3d	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3d2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3d	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3e1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3e	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3e2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3e	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3f1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3f	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3f2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3f	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3g1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3g	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3g2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3g	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3h1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3h	$S_4\times \He_3$	$C_2\times \He_3$	$54$	54.b1	$12$	9.a1	$72$	$9$	$1$
648.557.3h2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3h	$S_4\times \He_3$	$C_2\times \He_3$	$54$	54.b1	$12$	9.a1	$72$	$9$	$1$
648.557.3i1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3i	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3i2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3i	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3j1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3j	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3j2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3j	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3k1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3k	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3k2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3k	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3l1	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3l	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.3l2	$3$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.3l	$S_4\times \He_3$	$C_3\times S_4$	$72$	72.a1	$9$	24.a1	$27$	$24$	$1$
648.557.6a1	$6$	C	$3$	\(\Q(\sqrt{-3}) \)	648.557.6a	$S_4\times \He_3$	$S_3\times \He_3$	$162$	162.a1	$4$	54.a1	$12$	$54$	$1$