Elliptic curve isogeny class 27648.4-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.4-f
• Conductor: 27648.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 27648.4-f over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.4-f contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
27648.4-f1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 27\) , \( 31 a + 35\bigr] \)
27648.4-f2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a + 11\) , \( -17 a - 13\bigr] \)
27648.4-f3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1606 a - 2213\) , \( -43809 a - 28957\bigr] \)
27648.4-f4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -326 a - 133\) , \( 2591 a - 1725\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph