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

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

Isogeny class 27225.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27225.5-a1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -333 a - 1342\) , \( -7650 a - 18298\bigr] \)
27225.5-a2	\( \bigl[1\) , \( 1\) , \( 1\) , \( -58 a + 33\) , \( -60 a - 1138\bigr] \)
27225.5-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( 697 a + 848\) , \( 4370 a - 16430\bigr] \)
27225.5-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -88 a + 68\) , \( -20 a - 620\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph