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

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

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

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

Rank

Rank: \( 2 \)

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 27648.3-c over \(\Q(\sqrt{-2}) \)

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

Curve label	Weierstrass Coefficients
27648.3-c1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a + 8\) , \( -2 a + 16\bigr] \)
27648.3-c2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3\) , \( a - 5\bigr] \)
27648.3-c3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 37\) , \( 55 a - 77\bigr] \)
27648.3-c4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 30 a + 63\) , \( 103 a - 161\bigr] \)