Elliptic curve isogeny class 576.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-576.2-a
• Conductor: 576.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 576.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 576.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
576.2-a1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -9 a + 8\) , \( 5 a - 18\bigr] \)
576.2-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 7 a + 9\) , \( -3 a + 11\bigr] \)
576.2-a3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4 a - 1\) , \( -2 a + 4\bigr] \)
576.2-a4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 2 a - 2\) , \( -5 a - 1\bigr] \)
576.2-a5	\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 1\) , \( a - 4\bigr] \)
576.2-a6	\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 1\) , \( a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph