Elliptic curve isogeny class 5184.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-5184.1-a
• Conductor: 5184.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 5184.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 5184.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5184.1-a1	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -18\) , \( -27 i\bigr] \)
5184.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \)
5184.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 39\) , \( -92 i\bigr] \)
5184.1-a4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 72\) , \( 275 i\bigr] \)

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