Elliptic curve isogeny class 160.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-160.2-a
• Conductor: 160.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 160.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 160.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
160.2-a1	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -37 i - 5\) , \( -88 i + 53\bigr] \)
160.2-a2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i + 1\) , \( i + 3\bigr] \)
160.2-a3	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 1\) , \( -i - 1\bigr] \)
160.2-a4	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -2 i\) , \( 2 i - 1\bigr] \)
160.2-a5	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -7 i + 5\) , \( 4 i + 7\bigr] \)
160.2-a6	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 2 i - 5\) , \( -4 i + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph