Elliptic curve isogeny class 9216.1-j over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-9216.1-j
• Conductor: 9216.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 9216.1-j over \(\Q(\sqrt{-1}) \)

Isogeny class 9216.1-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9216.1-j1	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -32 i\) , \( -360 i - 360\bigr] \)
9216.1-j2	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -2 i\) , \( 0\bigr] \)
9216.1-j3	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 8 i\) , \( 8 i + 8\bigr] \)
9216.1-j4	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 48 i\) , \( 72 i + 72\bigr] \)
9216.1-j5	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 128 i\) , \( 440 i + 440\bigr] \)
9216.1-j6	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 768 i\) , \( 5544 i + 5544\bigr] \)

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