Elliptic curve isogeny class 53361.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-53361.1-a
• Conductor: 53361.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 53361.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 53361.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
53361.1-a1	\( \bigl[i\) , \( -1\) , \( i\) , \( 32\) , \( 5578\bigr] \)
53361.1-a2	\( \bigl[i\) , \( -1\) , \( i\) , \( 127\) , \( -432\bigr] \)
53361.1-a3	\( \bigl[i\) , \( -1\) , \( i\) , \( -38\) , \( -36\bigr] \)
53361.1-a4	\( \bigl[i\) , \( -1\) , \( i\) , \( -283\) , \( 1924\bigr] \)
53361.1-a5	\( \bigl[i\) , \( -1\) , \( i\) , \( -33\) , \( -62\bigr] \)
53361.1-a6	\( \bigl[i\) , \( -1\) , \( i\) , \( -4518\) , \( 118810\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph