Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-81.1-b
Conductor 81.1
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 81.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 81.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
81.1-b1 \( \bigl[a\) , \( 1\) , \( 1\) , \( a - 3\) , \( -a + 1\bigr] \)
81.1-b2 \( \bigl[a\) , \( 1\) , \( 1\) , \( 13 a - 33\) , \( 54 a - 98\bigr] \)
81.1-b3 \( \bigl[a\) , \( 1\) , \( 1\) , \( -2 a - 3\) , \( a + 1\bigr] \)
81.1-b4 \( \bigl[a\) , \( 1\) , \( 1\) , \( -14 a - 33\) , \( -54 a - 98\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph