Elliptic curve isogeny class 1536.1-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1536.1-a
• Conductor: 1536.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 1536.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1536.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1536.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 5\) , \( 7 a - 5\bigr] \)
1536.1-a2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a\) , \( 0\bigr] \)
1536.1-a3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a\) , \( 4 a + 8\bigr] \)
1536.1-a4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 10\) , \( 2 a + 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph