Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-1458.1-k
Conductor 1458.1
Rank \( 1 \)

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 1458.1-k over \(\Q(\sqrt{2}) \)

Isogeny class 1458.1-k contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
1458.1-k1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
1458.1-k2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \)
1458.1-k3 \( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph