Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 64576.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 150000 over imaginary quadratic fields with absolute discriminant 3

Note: The completeness Only modular elliptic curves are included

Results (unique match)

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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
64576.1-a1	64576.1-a	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	64576.1	\( 2^{6} \cdot 1009 \)	\( 2^{16} \cdot 1009 \)	$2.46727$	$(-35a+27), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$0.092063472$	$3.123996783$	2.656790354	\( \frac{35840}{1009} a - \frac{8192}{1009} \)	\( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 1\) , \( -4 a - 1\bigr] \)	${y}^2={x}^{3}-a{x}^{2}+\left(-a+1\right){x}-4a-1$

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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.