Elliptic curve isogeny class 6912.1-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6912.1-c
• Conductor: 6912.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 6912.1-c over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.1-c contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
6912.1-c1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -24 a + 24\) , \( 16 a + 144\bigr] \)
6912.1-c2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a + 32\) , \( 4 a - 12\bigr] \)
6912.1-c3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -156 a - 480\) , \( -2284 a - 3628\bigr] \)
6912.1-c4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 80\) , \( -44 a + 244\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph