Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-9.1-a
Conductor 9.1
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 9.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 9.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -40 a - 60\) , \( -153 a - 220\bigr] \)
9.1-a2 \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
9.1-a3 \( \bigl[a\) , \( a\) , \( a + 1\) , \( -2 a - 3\) , \( 0\bigr] \)
9.1-a4 \( \bigl[a\) , \( a\) , \( a + 1\) , \( -162 a - 243\) , \( -1495 a - 2130\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph