Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-3969.1-b
Conductor 3969.1
Rank \( 0 \)

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Base field \(\Q(\sqrt{2}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).

Elliptic curves in class 3969.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 3969.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
3969.1-b1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \)
3969.1-b2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
3969.1-b3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \)
3969.1-b4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \)
3969.1-b5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \)
3969.1-b6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph