Elliptic curve isogeny class 57600.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57600.2-a
• Conductor: 57600.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 57600.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 57600.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
57600.2-a1	\( \bigl[0\) , \( -i\) , \( 0\) , \( 80\) , \( -2400 i\bigr] \)
57600.2-a2	\( \bigl[0\) , \( -i\) , \( 0\) , \( -80\) , \( 80 i\bigr] \)
57600.2-a3	\( \bigl[0\) , \( -i\) , \( 0\) , \( 20\) , \( 0\bigr] \)
57600.2-a4	\( \bigl[0\) , \( -i\) , \( 0\) , \( 200\) , \( -1152 i\bigr] \)
57600.2-a5	\( \bigl[0\) , \( -i\) , \( 0\) , \( 15\) , \( 18 i\bigr] \)
57600.2-a6	\( \bigl[0\) , \( -i\) , \( 0\) , \( 3200\) , \( -70752 i\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph