Elliptic curves over \(\Q(\sqrt{-3}) \) of conductor 523.2

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
523.2-a1	523.2-a	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	523.2	\( 523 \)	\( 523^{3} \)	$0.74016$	$(-26a+17)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1[2]	$1$	\( 3 \)	$1$	$2.284168151$	0.879176731	\( -\frac{11489855124637}{143055667} a + \frac{5361021673434}{143055667} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -16 a - 4\) , \( 23 a - 5\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-16a-4\right){x}+23a-5$
523.2-a2	523.2-a	$2$	$3$	\(\Q(\sqrt{-3}) \)	$2$	$[0, 1]$	523.2	\( 523 \)	\( 523 \)	$0.74016$	$(-26a+17)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1[2]	$1$	\( 1 \)	$1$	$6.852504454$	0.879176731	\( \frac{19832319}{523} a - \frac{8500193}{523} \)	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( a + 1\) , \( 1\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(a+1\right){x}+1$

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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.