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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-7056.2-c
• Conductor: 7056.2
• Rank: \( 0 \)

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

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

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

Isogeny class 7056.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
7056.2-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -113\) , \( 516\bigr] \)
7056.2-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
7056.2-c3	\( \bigl[a\) , \( 1\) , \( a\) , \( -6\) , \( -3\bigr] \)
7056.2-c4	\( \bigl[a\) , \( 1\) , \( a\) , \( -456\) , \( -3837\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph