Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-82.1-a
Conductor 82.1
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 82.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 82.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
82.1-a1 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -15 a - 79\) , \( -47 a - 251\bigr] \)
82.1-a2 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 1\) , \( -a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph