Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-89.1-b
Conductor 89.1
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 89.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 89.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
89.1-b1 \( \bigl[0\) , \( 1\) , \( a + 1\) , \( -18 a - 23\) , \( -60 a - 64\bigr] \)
89.1-b2 \( \bigl[0\) , \( 1\) , \( a + 1\) , \( 2 a - 3\) , \( -2 a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph