Elliptic curve isogeny class 198.6-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-198.6-a
• Conductor: 198.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 198.6-a over \(\Q(\sqrt{-2}) \)

Isogeny class 198.6-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
198.6-a1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -11 a + 42\) , \( 80 a + 86\bigr] \)
198.6-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2 a - 19\) , \( -2 a + 38\bigr] \)
198.6-a3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a + 1\) , \( -2 a + 2\bigr] \)
198.6-a4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -a + 2\) , \( 2 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph