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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-9216.1-d
• Conductor: 9216.1
• Rank: \( 0 \)

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

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

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

Isogeny class 9216.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.1-d1	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -16 i\) , \( 16 i + 16\bigr] \)
9216.1-d2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 4 i\) , \( 0\bigr] \)
9216.1-d3	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -8 i\) , \( 4 i - 4\bigr] \)
9216.1-d4	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 64 i\) , \( -120 i - 120\bigr] \)

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