Elliptic curves over \(\Q(\sqrt{-1}) \) of conductor 585.3

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 100000 over imaginary quadratic fields with absolute discriminant 4

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
585.3-a1	585.3-a	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	585.3	\( 3^{2} \cdot 5 \cdot 13 \)	\( 3^{2} \cdot 5 \cdot 13^{2} \)	$0.87894$	$(2a+1), (-3a-2), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2 \)	$0.103359645$	$5.757692776$	0.595113083	\( -\frac{23137792}{2535} a - \frac{31081664}{2535} \)	\( \bigl[i + 1\) , \( -1\) , \( 1\) , \( -3 i - 1\) , \( 2 i\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3i-1\right){x}+2i$
585.3-a2	585.3-a	$2$	$2$	\(\Q(\sqrt{-1}) \)	$2$	$[0, 1]$	585.3	\( 3^{2} \cdot 5 \cdot 13 \)	\( 3^{4} \cdot 5^{2} \cdot 13 \)	$0.87894$	$(2a+1), (-3a-2), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2^{2} \)	$0.051679822$	$5.757692776$	0.595113083	\( \frac{5298688}{2925} a - \frac{51776}{325} \)	\( \bigl[i + 1\) , \( 1\) , \( 1\) , \( i - 1\) , \( i - 1\bigr] \)	${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(i-1\right){x}+i-1$

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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.