Elliptic curve isogeny class 25921.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-25921.1-a
• Conductor: 25921.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 25921.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 25921.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
25921.1-a1	\( \bigl[i\) , \( 1\) , \( i\) , \( 27\) , \( -36\bigr] \)
25921.1-a2	\( \bigl[i\) , \( 1\) , \( i\) , \( -8\) , \( -8\bigr] \)
25921.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -2\bigr] \)
25921.1-a4	\( \bigl[i\) , \( 1\) , \( i\) , \( -123\) , \( -560\bigr] \)

Rank

Rank: \( 1 \)

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