Elliptic curve isogeny class 27648.2-bj over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.2-bj
• Conductor: 27648.2
• Rank: \( 1 \)

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

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

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

Elliptic curves in class 27648.2-bj over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.2-bj contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27648.2-bj1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -50 a + 43\) , \( -353 a + 253\bigr] \)
27648.2-bj2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a - 37\) , \( -51 a + 93\bigr] \)
27648.2-bj3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 28 a - 32\) , \( -86 a + 52\bigr] \)
27648.2-bj4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 290 a - 577\) , \( -3993 a + 4737\bigr] \)