Elliptic curve isogeny class 22500.8-bg over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-22500.8-bg
• Conductor: 22500.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 22500.8-bg over \(\Q(\sqrt{-11}) \)

Isogeny class 22500.8-bg contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
22500.8-bg1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
22500.8-bg2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -28\) , \( 272\bigr] \)
22500.8-bg3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -828\) , \( 9072\bigr] \)
22500.8-bg4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph