Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 5625.1

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
5625.1-CMb1	5625.1-CMb	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	5625.1	\( 3^{2} \cdot 5^{4} \)	\( 3^{6} \cdot 5^{16} \)	$1.34039$	$(-2a+1), (5)$	$0$	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓	✓		✓	$3, 5$	3B.1.1[2], 5Cn.0.1	$1$	\( 2^{2} \cdot 3 \)	$1$	$0.948390915$	1.460143333	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 156\bigr] \)	${y}^2+{y}={x}^{3}+156$
5625.1-CMa1	5625.1-CMa	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	5625.1	\( 3^{2} \cdot 5^{4} \)	\( 3^{6} \cdot 5^{4} \)	$1.34039$	$(-2a+1), (5)$	$2$	$\mathsf{trivial}$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓	✓		✓	$5$	5Cn.0.1	$1$	\( 2^{2} \)	$0.017703945$	$4.741954575$	1.551017859	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \)	${y}^2+{y}={x}^{3}+1$

 

  *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.