Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-686.1-c
Conductor 686.1
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 686.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 686.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
686.1-c1 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -31 a - 50\) , \( 121 a + 124\bigr] \)
686.1-c2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -a\) , \( -a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph