Elliptic curve isogeny class 27648.3-bu over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.3-bu
• Conductor: 27648.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 27648.3-bu over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.3-bu contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27648.3-bu1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a + 8\) , \( 2 a - 16\bigr] \)
27648.3-bu2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 3\) , \( -a + 5\bigr] \)
27648.3-bu3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 37\) , \( -55 a + 77\bigr] \)
27648.3-bu4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 30 a + 63\) , \( -103 a + 161\bigr] \)

Rank

Rank: \( 0 \)

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