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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6912.2-d
• 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-d over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
6912.2-d1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a + 11\) , \( -7 a + 7\bigr] \)
6912.2-d2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 40\) , \( -4 a + 100\bigr] \)
6912.2-d3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a\) , \( 8 a + 4\bigr] \)
6912.2-d4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 96 a\) , \( 332 a + 364\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph