Elliptic curve isogeny class 5202.9-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.9-a
• Conductor: 5202.9
• Rank: \( 2 \)

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

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

Elliptic curves in class 5202.9-a over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.9-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
5202.9-a1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 3 a - 5\) , \( -3 a - 1\bigr] \)
5202.9-a2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -3 a - 7\) , \( -2 a - 6\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph