Elliptic curve isogeny class 5000.1-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5000.1-c
• Conductor: 5000.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 5000.1-c over \(\Q(\sqrt{-2}) \)

Isogeny class 5000.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5000.1-c1	\( \bigl[a\) , \( -1\) , \( a\) , \( 83\) , \( 491\bigr] \)
5000.1-c2	\( \bigl[a\) , \( -1\) , \( a\) , \( -42\) , \( 116\bigr] \)
5000.1-c3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \)
5000.1-c4	\( \bigl[a\) , \( -1\) , \( a\) , \( -667\) , \( 6991\bigr] \)

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