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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27225.5-c
• 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-c over \(\Q(\sqrt{-2}) \)

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

Curve label	Weierstrass Coefficients
27225.5-c1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -37 a + 4\) , \( -79 a + 114\bigr] \)
27225.5-c2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -2 a - 1\) , \( -2 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph