Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 63504.1

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
63504.1-CMg1	63504.1-CMg	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{16} \cdot 3^{12} \cdot 7^{6} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.2.1	$1$	\( 1 \)	$1$	$0.702205805$	0.810837422	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 240 a - 444\bigr] \)	${y}^2={x}^{3}+240a-444$
63504.1-CMf1	63504.1-CMf	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{16} \cdot 3^{12} \cdot 7^{2} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.2.1	$1$	\( 1 \)	$1$	$1.343271382$	1.551076189	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -12 a + 60\bigr] \)	${y}^2={x}^{3}-12a+60$
63504.1-CMe1	63504.1-CMe	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{16} \cdot 3^{6} \cdot 7^{8} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	0	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$3$	3B.1.1[2]	$1$	\( 3^{3} \)	$1$	$0.879377541$	3.046253162	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -156 a + 220\bigr] \)	${y}^2={x}^{3}-156a+220$
63504.1-CMd1	63504.1-CMd	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{8} \cdot 3^{12} \cdot 7^{10} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	$0 \le r \le 2$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.2.1	$4$	\( 1 \)	$1$	$0.582709009$	2.691417628	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -633 a + 708\bigr] \)	${y}^2={x}^{3}-633a+708$
63504.1-CMc1	63504.1-CMc	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{8} \cdot 3^{12} \cdot 7^{2} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	0	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$7$	7Cs.2.1	$1$	\( 1 \)	$1$	$2.132310406$	2.462179974	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -3 a + 15\bigr] \)	${y}^2={x}^{3}-3a+15$
63504.1-CMb1	63504.1-CMb	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 7^{8} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	0	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$3$	3B.1.1[2]	$1$	\( 3^{2} \)	$1$	$1.395924834$	1.611875157	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -39 a + 55\bigr] \)	${y}^2={x}^{3}-39a+55$
63504.1-CMa1	63504.1-CMa	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	63504.1	\( 2^{4} \cdot 3^{4} \cdot 7^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 7^{4} \)	$2.45697$	$(-2a+1), (-3a+1), (2)$	$2$	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$3$	3B.1.1[2]	$1$	\( 3^{3} \)	$0.126487255$	$2.670308144$	4.680139142	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 3 a - 8\bigr] \)	${y}^2={x}^{3}+3a-8$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.