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

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

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
27648.3-bq1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -46 a + 427\) , \( -2223 a - 1075\bigr] \)
27648.3-bq2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 154 a - 373\) , \( -1847 a + 2605\bigr] \)
27648.3-bq3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -26 a - 13\) , \( -155 a + 85\bigr] \)
27648.3-bq4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -36 a - 18\) , \( -95 a + 70\bigr] \)