Elliptic curve isogeny class 48672.2-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-48672.2-c
• Conductor: 48672.2
• Rank: \( 2 \)

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

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

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 48672.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 48672.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
48672.2-c1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -26\) , \( 357\bigr] \)
48672.2-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -92\) , \( -18\bigr] \)
48672.2-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -234\) , \( -1296\bigr] \)
48672.2-c4	\( \bigl[a\) , \( 1\) , \( a\) , \( -935\) , \( 10868\bigr] \)