Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-5000.1-b
Conductor 5000.1
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 5000.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 5000.1-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
5000.1-b1 \( \bigl[a\) , \( 1\) , \( a\) , \( 1\) , \( -1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph