Elliptic curve isogeny class 6912.3-g over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6912.3-g
• Conductor: 6912.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 6912.3-g over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.3-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
6912.3-g1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -156 a - 168\) , \( -1224 a - 504\bigr] \)
6912.3-g2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -196 a - 8\) , \( 856 a - 1336\bigr] \)
6912.3-g3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -16 a - 8\) , \( -8 a - 40\bigr] \)
6912.3-g4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 2\) , \( 0\bigr] \)
6912.3-g5	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a + 4\) , \( -2 a - 10\bigr] \)
6912.3-g6	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 64 a + 32\) , \( -60 a - 300\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph