Elliptic curve isogeny class 20000.1-g over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-20000.1-g
• Conductor: 20000.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20000.1-g over \(\Q(\sqrt{-2}) \)

Isogeny class 20000.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
20000.1-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 25\) , \( 0\bigr] \)
20000.1-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -25\) , \( 0\bigr] \)
20000.1-g3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -68\) , \( 253\bigr] \)
20000.1-g4	\( \bigl[a\) , \( -1\) , \( a\) , \( -67\) , \( -184\bigr] \)

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