Elliptic curve isogeny class 324.1-a over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-324.1-a
• Conductor: 324.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 324.1-a over \(\Q(\sqrt{11}) \)

Isogeny class 324.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
324.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \)
324.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \)
324.1-a3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -222 a - 735\) , \( -3887 a - 12892\bigr] \)
324.1-a4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 2027 a - 6711\) , \( -90208 a + 299200\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph