Elliptic curve isogeny class 44100.5-o over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-44100.5-o
• Conductor: 44100.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 44100.5-o over \(\Q(\sqrt{-11}) \)

Isogeny class 44100.5-o contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
44100.5-o1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -81\) , \( 6561\bigr] \)
44100.5-o2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 729\) , \( -176985\bigr] \)
44100.5-o3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -41\) , \( -39\bigr] \)
44100.5-o4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -6451\) , \( 124931\bigr] \)
44100.5-o5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -2701\) , \( -52819\bigr] \)
44100.5-o6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -361\) , \( 2585\bigr] \)
44100.5-o7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -2681\) , \( -53655\bigr] \)
44100.5-o8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -5761\) , \( 167825\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph