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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57600.2-z
• 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-z over \(\Q(\sqrt{-1}) \)

Isogeny class 57600.2-z contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
57600.2-z1	\( \bigl[0\) , \( i\) , \( 0\) , \( -24\) , \( -24 i\bigr] \)
57600.2-z2	\( \bigl[0\) , \( i\) , \( 0\) , \( 6\) , \( 0\bigr] \)
57600.2-z3	\( \bigl[0\) , \( i\) , \( 0\) , \( 56\) , \( 180 i\bigr] \)
57600.2-z4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20\) , \( -42\bigr] \)

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