Elliptic curve isogeny class 9216.2-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-9216.2-c
• Conductor: 9216.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 9216.2-c over \(\Q(\sqrt{-11}) \)

Isogeny class 9216.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.2-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \)
9216.2-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
9216.2-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \)
9216.2-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph