Elliptic curve isogeny class 88200.2-k over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-88200.2-k
• Conductor: 88200.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 88200.2-k over \(\Q(\sqrt{-1}) \)

Isogeny class 88200.2-k contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
88200.2-k1	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 40\) , \( 3091 i\bigr] \)
88200.2-k2	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 1320\) , \( -14963 i\bigr] \)
88200.2-k3	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 430\) , \( -2013 i\bigr] \)
88200.2-k4	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 185\) , \( 976 i\bigr] \)
88200.2-k5	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 6100\) , \( -182319 i\bigr] \)
88200.2-k6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -735\) , \( 7920\bigr] \)

Rank

Rank: \( 1 \)

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