Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 1521.1

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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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
1521.1-CMb1	1521.1-CMb	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	1521.1	\( 3^{2} \cdot 13^{2} \)	\( 3^{6} \cdot 13^{10} \)	$0.96657$	$(-2a+1), (-4a+1)$	$0$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.5.1	$1$	\( 1 \)	$1$	$0.956447781$	1.104410767	\( 0 \)	\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -136 a + 165\bigr] \)	${y}^2+a{y}={x}^{3}-136a+165$
1521.1-CMa1	1521.1-CMa	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	1521.1	\( 3^{2} \cdot 13^{2} \)	\( 3^{6} \cdot 13^{4} \)	$0.96657$	$(-2a+1), (-4a+1)$	$0$	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$3, 13$	3B.1.1[2], 13Cs.5.1	$1$	\( 3 \)	$1$	$3.448521516$	1.327336550	\( 0 \)	\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -4 a + 2\bigr] \)	${y}^2+a{y}={x}^{3}-4a+2$

 

  *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.