Elliptic curve isogeny class 22275.8-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22275.8-a
• Conductor: 22275.8
• Rank: \( 2 \)

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

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

Elliptic curves in class 22275.8-a over \(\Q(\sqrt{-11}) \)

Isogeny class 22275.8-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
22275.8-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 7\) , \( -8\bigr] \)
22275.8-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -38\) , \( -44\bigr] \)
22275.8-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -263\) , \( 1666\bigr] \)
22275.8-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -533\) , \( -4598\bigr] \)

Rank

Rank: \( 2 \)

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