Elliptic curve isogeny class 4225.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-4225.5-a
• Conductor: 4225.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 4225.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 4225.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4225.5-a1	\( \bigl[1\) , \( 0\) , \( 0\) , \( 4\) , \( 1\bigr] \)
4225.5-a2	\( \bigl[i\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
4225.5-a3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -5 i + 44\) , \( 111 i + 23\bigr] \)
4225.5-a4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 5 i + 44\) , \( -111 i + 23\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph