Elliptic curve isogeny class 1024.1-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1024.1-b
• Conductor: 1024.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1024.1-b over \(\Q(\sqrt{-1}) \)

Isogeny class 1024.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1024.1-b1	\( \bigl[0\) , \( -i\) , \( 0\) , \( -10 i - 11\) , \( 23 i + 6\bigr] \)
1024.1-b2	\( \bigl[0\) , \( i\) , \( 0\) , \( 10 i - 11\) , \( -23 i + 6\bigr] \)
1024.1-b3	\( \bigl[0\) , \( i\) , \( 0\) , \( -1\) , \( -i\bigr] \)
1024.1-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph