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

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

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

Curve label	Weierstrass Coefficients
57600.2-e1	\( \bigl[0\) , \( -i\) , \( 0\) , \( -40 i + 20\) , \( -16 i + 102\bigr] \)
57600.2-e2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -200 i + 574\) , \( 4986 i + 2972\bigr] \)
57600.2-e3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -320 i + 134\) , \( 410 i - 2420\bigr] \)
57600.2-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -20 i + 34\) , \( 90 i + 20\bigr] \)
57600.2-e5	\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 i - 6\) , \( 16 i + 2\bigr] \)
57600.2-e6	\( \bigl[0\) , \( 1\) , \( 0\) , \( 40 i - 66\) , \( -170 i + 164\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph