Elliptic curve isogeny class 48400.2-j over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-48400.2-j
• Conductor: 48400.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 48400.2-j over \(\Q(\sqrt{-2}) \)

Isogeny class 48400.2-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
48400.2-j1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
48400.2-j2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -16\) , \( 24\bigr] \)
48400.2-j3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -116\) , \( -416\bigr] \)
48400.2-j4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -236\) , \( 1520\bigr] \)

Rank

Rank: \( 0 \)

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