Properties

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

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

Curve label Weierstrass Coefficients
1024.1-g1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
1024.1-g2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 20 a - 44\) , \( 92 a - 144\bigr] \)
1024.1-g3 \( \bigl[0\) , \( -a\) , \( 0\) , \( -4\) , \( 4 a\bigr] \)
1024.1-g4 \( \bigl[0\) , \( -a\) , \( 0\) , \( -20 a - 44\) , \( 92 a + 144\bigr] \)

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