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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57600.2-j
• Conductor: 57600.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
57600.2-j1	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -22 i + 15\) , \( -21 i - 183\bigr] \)
57600.2-j2	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -142 i - 345\) , \( -1485 i - 2175\bigr] \)
57600.2-j3	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 18 i + 15\) , \( 3 i - 39\bigr] \)
57600.2-j4	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -542 i + 375\) , \( -733 i - 6767\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph