Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-72.1-a
Conductor 72.1
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 72.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 72.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
72.1-a1 \( \bigl[a\) , \( -1\) , \( a\) , \( 510 a - 817\) , \( 7986 a - 11651\bigr] \)
72.1-a2 \( \bigl[a\) , \( -1\) , \( a\) , \( 3\) , \( -23\bigr] \)
72.1-a3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-a4 \( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( 0\bigr] \)
72.1-a5 \( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -5\bigr] \)
72.1-a6 \( \bigl[a\) , \( -1\) , \( a\) , \( -17\) , \( 27\bigr] \)
72.1-a7 \( \bigl[a\) , \( -1\) , \( a\) , \( -97\) , \( -347\bigr] \)
72.1-a8 \( \bigl[a\) , \( -1\) , \( a\) , \( -510 a - 817\) , \( -7986 a - 11651\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph