Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-47.2-a
Conductor 47.2
Rank \( 0 \)

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

Isogeny class 47.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
47.2-a1 \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -2 a - 3\) , \( -2 a - 3\bigr] \)
47.2-a2 \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a - 2\) , \( 18 a - 27\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph