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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22275.8-k
• Conductor: 22275.8
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
22275.8-k1	\( \bigl[1\) , \( -1\) , \( a\) , \( -878 a + 9936\) , \( 213150 a - 26991\bigr] \)
22275.8-k2	\( \bigl[1\) , \( -1\) , \( a\) , \( -68 a + 621\) , \( 3441 a - 990\bigr] \)
22275.8-k3	\( \bigl[1\) , \( -1\) , \( a\) , \( 742 a - 774\) , \( 15492 a + 11943\bigr] \)
22275.8-k4	\( \bigl[1\) , \( -1\) , \( a\) , \( -68 a + 126\) , \( -24 a - 693\bigr] \)

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