Elliptic curves over \(\Q(\sqrt{-7}) \) of conductor 11664.5

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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
11664.5-a1	11664.5-a	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{6} \)	$2.45697$	$(-a+1), (3)$	$2$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3Cn	$1$	\( 2^{2} \)	$0.055827493$	$3.904156338$	2.636187434	\( -1215 a + 1242 \)	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -3\) , \( -2\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}-3{x}-2$
11664.5-b1	11664.5-b	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{6} \)	$2.45697$	$(-a+1), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3Cn	$1$	\( 1 \)	$0.423849156$	$3.041980706$	1.949300302	\( 110592 \)	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 9 a - 3\) , \( 6 a + 10\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}+\left(9a-3\right){x}+6a+10$
11664.5-c1	11664.5-c	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{18} \)	$2.45697$	$(-a+1), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3Cn	$1$	\( 2 \cdot 3 \)	$0.196253347$	$1.348697722$	2.401009724	\( 27 \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -6 a + 2\) , \( 20 a + 36\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-6a+2\right){x}+20a+36$
11664.5-d1	11664.5-d	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{18} \)	$2.45697$	$(-a+1), (3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3Cn	$1$	\( 1 \)	$1$	$1.301385446$	0.983754928	\( 1215 a + 27 \)	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -6 a + 29\) , \( 47 a - 18\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-6a+29\right){x}+47a-18$
11664.5-e1	11664.5-e	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{6} \)	$2.45697$	$(-a+1), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3Cn	$1$	\( 2 \)	$0.369539350$	$4.046093166$	4.521031537	\( 27 \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 0\) , \( -a - 1\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}-a-1$
11664.5-f1	11664.5-f	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{6} \)	$2.45697$	$(-a+1), (3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3Cn	$1$	\( 1 \)	$1$	$3.904156338$	2.951264786	\( 1215 a + 27 \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3\) , \( -a + 2\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+3{x}-a+2$
11664.5-g1	11664.5-g	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{18} \)	$2.45697$	$(-a+1), (3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3Cn	$1$	\( 2^{2} \)	$1$	$1.301385446$	3.935019714	\( -1215 a + 1242 \)	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -27\) , \( -21 a + 61\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}-27{x}-21a+61$
11664.5-h1	11664.5-h	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	11664.5	\( 2^{4} \cdot 3^{6} \)	\( 2^{12} \cdot 3^{18} \)	$2.45697$	$(-a+1), (3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$3$	3Cn	$1$	\( 3 \)	$1.618942499$	$1.013993568$	7.445585420	\( 110592 \)	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 81 a - 27\) , \( -183 a - 263\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}+\left(81a-27\right){x}-183a-263$

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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.