Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-1922.1-a
Conductor 1922.1
Rank \( 1 \)

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 1922.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1922.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1922.1-a1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \)
1922.1-a2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)
1922.1-a3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -21\) , \( 41\bigr] \)
1922.1-a4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -331\) , \( 2397\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph