Elliptic curve isogeny class 11025.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-11025.2-c
• Conductor: 11025.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 11025.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 11025.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
11025.2-c1	\( \bigl[i\) , \( 0\) , \( i\) , \( 18\) , \( 37\bigr] \)
11025.2-c2	\( \bigl[i\) , \( 0\) , \( i\) , \( -7\) , \( 7\bigr] \)
11025.2-c3	\( \bigl[i\) , \( 0\) , \( i\) , \( -2\) , \( -1\bigr] \)
11025.2-c4	\( \bigl[i\) , \( 0\) , \( i\) , \( -112\) , \( 469\bigr] \)

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