Elliptic curves over \(\Q(\sqrt{-5}) \) of conductor 69.3

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 1000 over imaginary quadratic fields with absolute discriminant 20

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
69.3-a1	69.3-a	$1$	$1$	\(\Q(\sqrt{-5}) \)	$2$	$[0, 1]$	69.3	\( 3 \cdot 23 \)	\( 3^{5} \cdot 23 \)	$1.15177$	$(3,a+2), (23,a+8)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$0.121721655$	$6.623670922$	0.721126726	\( -\frac{1665535}{5589} a + \frac{10944332}{5589} \)	\( \bigl[a\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+a{x}{y}+{y}={x}^3+{x}^2$
69.3-b1	69.3-b	$1$	$1$	\(\Q(\sqrt{-5}) \)	$2$	$[0, 1]$	69.3	\( 3 \cdot 23 \)	\( 3^{5} \cdot 23 \)	$1.15177$	$(3,a+2), (23,a+8)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 5 \)	$0.070567638$	$6.623670922$	2.090351553	\( -\frac{1665535}{5589} a + \frac{10944332}{5589} \)	\( \bigl[1\) , \( 0\) , \( a\) , \( 0\) , \( 1\bigr] \)	${y}^2+{x}{y}+a{y}={x}^3+1$

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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.