Elliptic curve isogeny class 6400.2-f over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-6400.2-f
• Conductor: 6400.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 6400.2-f over \(\Q(\sqrt{-1}) \)

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

Curve label	Weierstrass Coefficients
6400.2-f1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -2\bigr] \)
6400.2-f2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20 i + 10\) , \( -2 i - 36\bigr] \)
6400.2-f3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 20 i + 10\) , \( 2 i - 36\bigr] \)
6400.2-f4	\( \bigl[0\) , \( i\) , \( 0\) , \( 6\) , \( -4 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph