Elliptic curve isogeny class 25992.5-j over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-25992.5-j
• Conductor: 25992.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 25992.5-j over \(\Q(\sqrt{-2}) \)

Isogeny class 25992.5-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
25992.5-j1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 142\) , \( 546\bigr] \)
25992.5-j2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -48\) , \( 90\bigr] \)
25992.5-j3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -318\) , \( -2070\bigr] \)
25992.5-j4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -43\) , \( 116\bigr] \)

Rank

Rank: \( 1 \)

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