Elliptic curve isogeny class 6400.2-k over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-6400.2-k
• Conductor: 6400.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6400.2-k over \(\Q(\sqrt{-11}) \)

Isogeny class 6400.2-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
6400.2-k1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \)
6400.2-k2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \)
6400.2-k3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
6400.2-k4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph