Elliptic curve isogeny class 28224.2-c over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-28224.2-c
• Conductor: 28224.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 28224.2-c over \(\Q(\sqrt{-11}) \)

Isogeny class 28224.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28224.2-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
28224.2-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -392\) , \( -228\bigr] \)
28224.2-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -252\) , \( 1620\bigr] \)
28224.2-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4032\) , \( 99900\bigr] \)

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