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

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

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

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

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

Isogeny class 57600.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
57600.1-d1	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 62 i + 47\) , \( 1917 i + 313\bigr] \)
57600.1-d2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i + 2\) , \( 3 i + 2\bigr] \)
57600.1-d3	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -18 i - 13\) , \( -27 i + 5\bigr] \)
57600.1-d4	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -98 i - 73\) , \( 493 i + 145\bigr] \)
57600.1-d5	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -258 i - 193\) , \( 2163 i + 247\bigr] \)
57600.1-d6	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -1538 i - 1153\) , \( 32029 i + 6697\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph