Elliptic curve isogeny class 27225.5-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27225.5-d
• Conductor: 27225.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 27225.5-d over \(\Q(\sqrt{-2}) \)

Isogeny class 27225.5-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27225.5-d1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 36 a + 4\) , \( 78 a + 114\bigr] \)
27225.5-d2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( a - 1\) , \( a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph