Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-1584.2-a
Conductor 1584.2
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 1584.2-a over \(\Q(\sqrt{-11}) \)

Isogeny class 1584.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1584.2-a1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -77\) , \( 330\bigr] \)
1584.2-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 155 a - 127\) , \( 1031 a + 601\bigr] \)
1584.2-a3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -155 a + 28\) , \( -1031 a + 1632\bigr] \)
1584.2-a4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -1292\) , \( 18312\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph