Elliptic curve isogeny class 57600.1-m over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57600.1-m
• Conductor: 57600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 57600.1-m over \(\Q(\sqrt{-1}) \)

Isogeny class 57600.1-m contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
57600.1-m1	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 30 i + 23\) , \( -57 i + 7\bigr] \)
57600.1-m2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -10 i - 7\) , \( -9 i - 7\bigr] \)
57600.1-m3	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 18 i + 13\) , \( 17 i - 39\bigr] \)
57600.1-m4	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -130 i - 97\) , \( 789 i + 217\bigr] \)

Rank

Rank: \( 0 \)

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