Elliptic curves over \(\Q(\sqrt{3}) \) of conductor 968.1

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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
968.1-a1	968.1-a	$1$	$1$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	968.1	\( 2^{3} \cdot 11^{2} \)	\( 2^{4} \cdot 11^{2} \)	$1.72662$	$(a+1), (-2a+1), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	\( 2 \)	$0.040264364$	$36.16801486$	1.681569756	\( -\frac{27648}{11} \)	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 4 a - 7\) , \( -8 a + 12\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}+\left(4a-7\right){x}-8a+12$
968.1-b1	968.1-b	$1$	$1$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	968.1	\( 2^{3} \cdot 11^{2} \)	\( 2^{4} \cdot 11^{2} \)	$1.72662$	$(a+1), (-2a+1), (2a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	\( 2 \)	$1$	$5.480854942$	3.164373076	\( -\frac{27648}{11} \)	\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 4 a - 7\) , \( 7 a - 14\bigr] \)	${y}^2+\left(a+1\right){y}={x}^{3}+\left(4a-7\right){x}+7a-14$

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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.