Elliptic curve isogeny class 8100.8-g over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-8100.8-g
• Conductor: 8100.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 8100.8-g over \(\Q(\sqrt{-11}) \)

Isogeny class 8100.8-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
8100.8-g1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -69\) , \( -235\bigr] \)
8100.8-g2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 6\) , \( 0\bigr] \)
8100.8-g3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -24\) , \( 18\bigr] \)
8100.8-g4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1149\) , \( -14707\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph