Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-4356.1-a
Conductor 4356.1
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 4356.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 4356.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4356.1-a1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -77\) , \( 330\bigr] \)
4356.1-a2 \( \bigl[a\) , \( -1\) , \( 0\) , \( -323\) , \( 2289\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph