Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 23716.1

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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
23716.1-a1	23716.1-a	$4$	$6$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	23716.1	\( 2^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{4} \cdot 7^{6} \cdot 11^{12} \)	$1.92070$	$(-3a+1), (2), (11)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B[2]	$1$	\( 2^{3} \)	$1$	$0.373899960$	0.863484971	\( \frac{13060888875}{7086244} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( -392 a + 245\) , \( 300 a - 555\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-392a+245\right){x}+300a-555$
23716.1-a2	23716.1-a	$4$	$6$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	23716.1	\( 2^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{24} \cdot 7^{6} \cdot 11^{2} \)	$1.92070$	$(-3a+1), (2), (11)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B[2]	$1$	\( 2^{2} \)	$1$	$0.747799921$	0.863484971	\( \frac{1108717875}{45056} \)	\( \bigl[a\) , \( -1\) , \( 1\) , \( 64 a - 172\) , \( -465 a + 860\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(64a-172\right){x}-465a+860$
23716.1-a3	23716.1-a	$4$	$6$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	23716.1	\( 2^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{8} \cdot 7^{6} \cdot 11^{6} \)	$1.92070$	$(-3a+1), (2), (11)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B[2]	$1$	\( 2^{2} \)	$1$	$0.747799921$	0.863484971	\( \frac{2714704875}{21296} \)	\( \bigl[1\) , \( a\) , \( 0\) , \( -232 a + 145\) , \( -740 a + 1369\bigr] \)	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-232a+145\right){x}-740a+1369$
23716.1-a4	23716.1-a	$4$	$6$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	23716.1	\( 2^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{12} \cdot 7^{6} \cdot 11^{4} \)	$1.92070$	$(-3a+1), (2), (11)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B[2]	$1$	\( 2^{3} \)	$1$	$0.373899960$	0.863484971	\( \frac{4406910829875}{7744} \)	\( \bigl[a\) , \( -1\) , \( 1\) , \( 1024 a - 2732\) , \( -28625 a + 52956\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(1024a-2732\right){x}-28625a+52956$

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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.