Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-1024.1-h
Conductor 1024.1
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 1024.1-h over \(\Q(\sqrt{2}) \)

Isogeny class 1024.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1024.1-h1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2\) , \( a - 2\bigr] \)
1024.1-h2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -30 a - 53\) , \( 105 a + 141\bigr] \)
1024.1-h3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 13\) , \( -19 a - 27\bigr] \)
1024.1-h4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 30 a - 53\) , \( -105 a + 141\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph