Elliptic curve isogeny class 27225.6-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27225.6-a
• Conductor: 27225.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 27225.6-a over \(\Q(\sqrt{-2}) \)

Isogeny class 27225.6-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
27225.6-a1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 491 a + 557\) , \( -1542 a + 10053\bigr] \)
27225.6-a2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -293 a - 787\) , \( 4744 a + 7519\bigr] \)
27225.6-a3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -9 a + 11\) , \( 197 a + 1107\bigr] \)
27225.6-a4	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -83 a - 185\) , \( -527 a - 1154\bigr] \)
27225.6-a5	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 113 a + 151\) , \( 89 a - 1308\bigr] \)
27225.6-a6	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -237 a + 277\) , \( -639 a - 3282\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 18 & 2 & 6 \\ 9 & 1 & 3 & 2 & 18 & 6 \\ 3 & 3 & 1 & 6 & 6 & 2 \\ 18 & 2 & 6 & 1 & 9 & 3 \\ 2 & 18 & 6 & 9 & 1 & 3 \\ 6 & 6 & 2 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph