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

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

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

Curve label	Weierstrass Coefficients
57600.2-h1	\( \bigl[0\) , \( -i\) , \( 0\) , \( -160 i - 160\) , \( -1156 i - 552\bigr] \)
57600.2-h2	\( \bigl[0\) , \( -i\) , \( 0\) , \( -10 i - 10\) , \( -16 i - 12\bigr] \)
57600.2-h3	\( \bigl[0\) , \( -i\) , \( 0\) , \( 20 i - 20\) , \( -92 i + 40\bigr] \)
57600.2-h4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 i - 1\) , \( -10 i - 5\bigr] \)

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