Elliptic curve isogeny class 45000.3-o over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-45000.3-o
• Conductor: 45000.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 45000.3-o over \(\Q(\sqrt{-1}) \)

Isogeny class 45000.3-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
45000.3-o1	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 23\) , \( 23 i\bigr] \)
45000.3-o2	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 102\) , \( 148 i\bigr] \)
45000.3-o3	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 852\) , \( -9602 i\bigr] \)
45000.3-o4	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 1352\) , \( 18898 i\bigr] \)

Rank

Rank: \( 0 \)

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