Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 51984.3

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 (displaying both matches)

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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
51984.3-CMb1	51984.3-CMb	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	51984.3	\( 2^{4} \cdot 3^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 19^{8} \)	$2.33704$	$(-2a+1), (-5a+2), (2)$	$0 \le r \le 2$	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$3$	3B.1.1[2]	$4$	\( 3^{2} \)	$1$	$0.717394968$	3.313505425	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -231 a - 185\bigr] \)	${y}^2={x}^{3}-231a-185$
51984.3-CMa1	51984.3-CMa	$1$	$1$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	51984.3	\( 2^{4} \cdot 3^{2} \cdot 19^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 19^{4} \)	$2.33704$	$(-2a+1), (-5a+2), (2)$	0	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓			✓	$3$	3B.1.1[2]	$1$	\( 3^{2} \)	$1$	$1.914297916$	2.210440835	\( 0 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -21 a + 16\bigr] \)	${y}^2={x}^{3}-21a+16$

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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.