Elliptic curve isogeny class 7200.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-7200.2-a
• Conductor: 7200.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 7200.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 7200.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7200.2-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 6\) , \( 3\bigr] \)
7200.2-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 0\bigr] \)
7200.2-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( -13\) , \( -22\bigr] \)
7200.2-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -20\) , \( 42\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph