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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-48672.2-h
• Conductor: 48672.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
48672.2-h1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -26\) , \( -357\bigr] \)
48672.2-h2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -92\) , \( 18\bigr] \)
48672.2-h3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -234\) , \( 1296\bigr] \)
48672.2-h4	\( \bigl[a\) , \( 0\) , \( a\) , \( -935\) , \( -10867\bigr] \)

Rank

Rank: \( 1 \)

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