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

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

Isogeny class 44100.5-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
44100.5-e1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 7\) , \( 147\bigr] \)
44100.5-e2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \)
44100.5-e3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -23\) , \( 33\bigr] \)
44100.5-e4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -373\) , \( 2623\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph