Elliptic curve isogeny class 7225.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-7225.5-a
• Conductor: 7225.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 7225.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 7225.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7225.5-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -3\) , \( -22\bigr] \)
7225.5-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -95 i + 37\) , \( 59 i - 360\bigr] \)
7225.5-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 95 i + 37\) , \( -59 i - 360\bigr] \)
7225.5-a4	\( \bigl[i\) , \( -1\) , \( 0\) , \( -8\) , \( 13\bigr] \)

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