Elliptic curve isogeny class 7056.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-7056.2-a
• Conductor: 7056.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 7056.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 7056.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
7056.2-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -136\) , \( -1736\bigr] \)
7056.2-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
7056.2-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -16\) , \( -8\bigr] \)
7056.2-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -156\) , \( 720\bigr] \)
7056.2-a5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -196\) , \( -1088\bigr] \)
7056.2-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -3136\) , \( -68120\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph