Elliptic curves over \(\Q(\sqrt{-10}) \) of conductor 44.2

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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
44.2-a1	44.2-a	$2$	$3$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	44.2	\( 2^{2} \cdot 11 \)	\( 2^{8} \cdot 11 \)	$1.45557$	$(2,a), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 3 \)	$1$	$7.146887379$	0.753348076	\( \frac{1372}{11} a + \frac{1372}{11} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 1\bigr] \)	${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(a-2\right){x}+1$
44.2-a2	44.2-a	$2$	$3$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	44.2	\( 2^{2} \cdot 11 \)	\( 2^{8} \cdot 11^{3} \)	$1.45557$	$(2,a), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 1 \)	$1$	$2.382295793$	0.753348076	\( \frac{3109029596}{1331} a + \frac{9318326932}{1331} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -9 a + 18\) , \( -4 a - 131\bigr] \)	${y}^2+a{x}{y}={x}^3+\left(-a+1\right){x}^2+\left(-9a+18\right){x}-4a-131$
44.2-b1	44.2-b	$2$	$3$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	44.2	\( 2^{2} \cdot 11 \)	\( 2^{20} \cdot 11 \)	$1.45557$	$(2,a), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 1 \)	$1$	$7.146887379$	2.260044229	\( \frac{1372}{11} a + \frac{1372}{11} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -1\) , \( -a + 2\bigr] \)	${y}^2={x}^3-a{x}^2-{x}-a+2$
44.2-b2	44.2-b	$2$	$3$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	44.2	\( 2^{2} \cdot 11 \)	\( 2^{20} \cdot 11^{3} \)	$1.45557$	$(2,a), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 3 \)	$1$	$2.382295793$	2.260044229	\( \frac{3109029596}{1331} a + \frac{9318326932}{1331} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a + 79\) , \( -9 a + 578\bigr] \)	${y}^2={x}^3-a{x}^2+\left(-40a+79\right){x}-9a+578$

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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.