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

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

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

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

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

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

Curve label	Weierstrass Coefficients
57600.2-f1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -30\bigr] \)
57600.2-f2	\( \bigl[0\) , \( -i\) , \( 0\) , \( 80\) , \( 168 i\bigr] \)
57600.2-f3	\( \bigl[0\) , \( -i\) , \( 0\) , \( 30\) , \( -72 i\bigr] \)
57600.2-f4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 120 i + 94\) , \( 114 i - 732\bigr] \)
57600.2-f5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -120 i + 94\) , \( -114 i - 732\bigr] \)
57600.2-f6	\( \bigl[0\) , \( -i\) , \( 0\) , \( 480\) , \( -4212 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph