Elliptic curve isogeny class 81225.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-81225.2-c
• Conductor: 81225.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 81225.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 81225.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
81225.2-c1	\( \bigl[i\) , \( -1\) , \( 0\) , \( 23\) , \( 176\bigr] \)
81225.2-c2	\( \bigl[i\) , \( -1\) , \( 0\) , \( -1237\) , \( -13054\bigr] \)
81225.2-c3	\( \bigl[i\) , \( -1\) , \( 0\) , \( -382\) , \( 2849\bigr] \)
81225.2-c4	\( \bigl[i\) , \( -1\) , \( 0\) , \( -6007\) , \( 181724\bigr] \)

Rank

Rank: \( 1 \)

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