Elliptic curve isogeny class 2304.1-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-2304.1-c
• Conductor: 2304.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2304.1-c over \(\Q(\sqrt{-1}) \)

Isogeny class 2304.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2304.1-c1	\( \bigl[0\) , \( -i\) , \( 0\) , \( -16\) , \( 180 i\bigr] \)
2304.1-c2	\( \bigl[0\) , \( i\) , \( 0\) , \( -1\) , \( 0\bigr] \)
2304.1-c3	\( \bigl[0\) , \( -i\) , \( 0\) , \( 4\) , \( -4 i\bigr] \)
2304.1-c4	\( \bigl[0\) , \( i\) , \( 0\) , \( 24\) , \( -36 i\bigr] \)
2304.1-c5	\( \bigl[0\) , \( -i\) , \( 0\) , \( 64\) , \( -220 i\bigr] \)
2304.1-c6	\( \bigl[0\) , \( i\) , \( 0\) , \( 384\) , \( -2772 i\bigr] \)

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