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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-22050.2-d
• 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-d over \(\Q(\sqrt{-2}) \)

Isogeny class 22050.2-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
22050.2-d1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -119300\) , \( -16229850\bigr] \)
22050.2-d2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1270\) , \( -789048\bigr] \)
22050.2-d3	\( \bigl[1\) , \( 0\) , \( 0\) , \( 210\) , \( 900\bigr] \)
22050.2-d4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \)
22050.2-d5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -7550\) , \( -247500\bigr] \)
22050.2-d6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -15070\) , \( 710612\bigr] \)
22050.2-d7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -120050\) , \( -16020000\bigr] \)
22050.2-d8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1920800\) , \( -1024800150\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph