Elliptic curve isogeny class 6912.2-i over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6912.2-i
• Conductor: 6912.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6912.2-i over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.2-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
6912.2-i1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 196 a - 8\) , \( 856 a + 1336\bigr] \)
6912.2-i2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 156 a - 168\) , \( -1224 a + 504\bigr] \)
6912.2-i3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 16 a - 8\) , \( -8 a + 40\bigr] \)
6912.2-i4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a + 2\) , \( 0\bigr] \)
6912.2-i5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a + 4\) , \( -2 a + 10\bigr] \)
6912.2-i6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -64 a + 32\) , \( -60 a + 300\bigr] \)

Rank

Rank: \( 1 \)

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