Elliptic curves over \(\Q(\sqrt{-39}) \) of conductor 144.3

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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
144.3-a1	144.3-a	$4$	$6$	\(\Q(\sqrt{-39}) \)	$2$	$[0, 1]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{18} \)	$1.93313$	$(2,a), (2,a+1), (3,a+1)$	0	$\Z/2\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \)	$1$	$5.108115717$	1.635906278	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -27\bigr] \)	${y}^2={x}^3-27$
144.3-a2	144.3-a	$4$	$6$	\(\Q(\sqrt{-39}) \)	$2$	$[0, 1]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( 2^{8} \cdot 3^{6} \)	$1.93313$	$(2,a), (2,a+1), (3,a+1)$	0	$\Z/6\Z$	$\textsf{potential}$	$-3$	$N(\mathrm{U}(1))$	✓	✓		✓	$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \cdot 3^{2} \)	$1$	$5.108115717$	1.635906278	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \)	${y}^2={x}^3+1$
144.3-a3	144.3-a	$4$	$6$	\(\Q(\sqrt{-39}) \)	$2$	$[0, 1]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{6} \)	$1.93313$	$(2,a), (2,a+1), (3,a+1)$	0	$\Z/6\Z$	$\textsf{potential}$	$-12$	$N(\mathrm{U}(1))$	✓	✓		✓	$2, 3$	2B, 3B.1.1	$4$	\( 2 \cdot 3^{2} \)	$1$	$2.554057858$	1.635906278	\( 54000 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \)	${y}^2={x}^3-15{x}+22$
144.3-a4	144.3-a	$4$	$6$	\(\Q(\sqrt{-39}) \)	$2$	$[0, 1]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{18} \)	$1.93313$	$(2,a), (2,a+1), (3,a+1)$	0	$\Z/2\Z$	$\textsf{potential}$	$-12$	$N(\mathrm{U}(1))$	✓	✓		✓	$2, 3$	2B, 3B.1.1	$4$	\( 2 \)	$1$	$2.554057858$	1.635906278	\( 54000 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -135\) , \( -594\bigr] \)	${y}^2={x}^3-135{x}-594$

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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.