Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-34.1-a
Conductor 34.1
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 34.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 34.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
34.1-a1 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -16 a + 19\) , \( -25 a + 31\bigr] \)
34.1-a2 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 2 a + 4\) , \( 0\bigr] \)
34.1-a3 \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -8 a - 16\) , \( -10 a - 4\bigr] \)
34.1-a4 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 64 a - 141\) , \( -457 a + 479\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph