Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-219.2-a
Conductor 219.2
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 219.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 219.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
219.2-a1 \( \bigl[a\) , \( -a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
219.2-a2 \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph