Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-22050.2-d
Conductor 22050.2
Rank not recorded

Related objects

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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 not yet determined.

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