Elliptic curve isogeny class 27225.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27225.2-a
• Conductor: 27225.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 27225.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 27225.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27225.2-a1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 148 a - 75\) , \( 926 a + 437\bigr] \)
27225.2-a2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -22 a - 107\) , \( -75 a - 489\bigr] \)
27225.2-a3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 30 a + 101\) , \( -289 a + 347\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph