Elliptic curve isogeny class 28224.1-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-28224.1-d
• Conductor: 28224.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 28224.1-d over \(\Q(\sqrt{-1}) \)

Isogeny class 28224.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28224.1-d1	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 12\) , \( -23 i\bigr] \)
28224.1-d2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -22\) , \( -40\bigr] \)
28224.1-d3	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 28\) , \( 49 i\bigr] \)
28224.1-d4	\( \bigl[0\) , \( -i\) , \( 0\) , \( 84\) , \( 270 i\bigr] \)

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