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

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-44100.5-r
• 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-r over \(\Q(\sqrt{-11}) \)

Isogeny class 44100.5-r contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
44100.5-r1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -119300\) , \( -16229850\bigr] \)
44100.5-r2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1270\) , \( -789048\bigr] \)
44100.5-r3	\( \bigl[1\) , \( 0\) , \( 0\) , \( 210\) , \( 900\bigr] \)
44100.5-r4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \)
44100.5-r5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -7550\) , \( -247500\bigr] \)
44100.5-r6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -15070\) , \( 710612\bigr] \)
44100.5-r7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -120050\) , \( -16020000\bigr] \)
44100.5-r8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1920800\) , \( -1024800150\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph