Elliptic curve isogeny class 22050.2-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-22050.2-c
• Conductor: 22050.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 22050.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 22050.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
22050.2-c1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -980\) , \( -15325\bigr] \)
22050.2-c2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 10\) , \( -13\bigr] \)
22050.2-c3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -205\bigr] \)
22050.2-c4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -370\) , \( 2435\bigr] \)
22050.2-c5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1050\) , \( -13533\bigr] \)
22050.2-c6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -16800\) , \( -845133\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph