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

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

Isogeny class 57600.2-ba contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
57600.2-ba1	\( \bigl[0\) , \( i\) , \( 0\) , \( 216\) , \( 4080 i\bigr] \)
57600.2-ba2	\( \bigl[0\) , \( i\) , \( 0\) , \( -24\) , \( -144 i\bigr] \)
57600.2-ba3	\( \bigl[0\) , \( i\) , \( 0\) , \( 7256\) , \( 34800 i\bigr] \)
57600.2-ba4	\( \bigl[0\) , \( i\) , \( 0\) , \( 1096\) , \( 12400 i\bigr] \)
57600.2-ba5	\( \bigl[0\) , \( i\) , \( 0\) , \( 296\) , \( -1680 i\bigr] \)
57600.2-ba6	\( \bigl[0\) , \( i\) , \( 0\) , \( 5336\) , \( 151536 i\bigr] \)
57600.2-ba7	\( \bigl[0\) , \( i\) , \( 0\) , \( 4616\) , \( -119184 i\bigr] \)
57600.2-ba8	\( \bigl[0\) , \( i\) , \( 0\) , \( 85336\) , \( 9623536 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph