Elliptic curves over \(\Q(\sqrt{-11}) \) of conductor 8281.1

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 50000 over imaginary quadratic fields with absolute discriminant 11

Note: The completeness Only modular elliptic curves are included

Results (4 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
8281.1-a1	8281.1-a	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{2} \cdot 13^{2} \)	$2.82719$	$(7), (13)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.1	$1$	\( 1 \)	$1.059245086$	$4.379860585$	0.621695729	\( -\frac{43614208}{91} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -7\) , \( 5\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}-7{x}+5$
8281.1-a2	8281.1-a	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{18} \cdot 13^{2} \)	$2.82719$	$(7), (13)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3B.1.2	$1$	\( 3^{2} \)	$0.117693898$	$0.486651176$	0.621695729	\( -\frac{178643795968}{524596891} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}-117{x}-1245$
8281.1-a3	8281.1-a	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{6} \cdot 13^{6} \)	$2.82719$	$(7), (13)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	\( 3^{2} \)	$0.353081695$	$1.459953528$	0.621695729	\( \frac{224755712}{753571} \)	\( \bigl[0\) , \( 1\) , \( 1\) , \( 13\) , \( 42\bigr] \)	${y}^2+{y}={x}^{3}+{x}^{2}+13{x}+42$
8281.1-b1	8281.1-b	$1$	$1$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	8281.1	\( 7^{2} \cdot 13^{2} \)	\( 7^{2} \cdot 13^{2} \)	$2.82719$	$(7), (13)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓				$1$	\( 1 \)	$0.142392150$	$6.505570680$	1.117210729	\( \frac{110592}{91} \)	\( \bigl[0\) , \( 0\) , \( 1\) , \( 1\) , \( 0\bigr] \)	${y}^2+{y}={x}^{3}+{x}$

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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.