Elliptic curve isogeny class 16200.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-16200.2-c
• Conductor: 16200.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 16200.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 16200.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
16200.2-c1	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 180\) , \( 8100 i\bigr] \)
16200.2-c2	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -180\) , \( -270 i\bigr] \)
16200.2-c3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 45\) , \( 0\bigr] \)
16200.2-c4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 450\) , \( 3888 i\bigr] \)
16200.2-c5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -138\) , \( -623\bigr] \)
16200.2-c6	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 7200\) , \( 238788 i\bigr] \)

Rank

Rank: \( 0 \)

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