Elliptic curve isogeny class 1584.2-a over number field \(\Q(\sqrt{-11}) \)

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

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