Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-4050.1-a
Conductor 4050.1
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 4050.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 4050.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
4050.1-a1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -122\) , \( 1721\bigr] \)
4050.1-a2 \( \bigl[1\) , \( -1\) , \( 1\) , \( 13\) , \( -61\bigr] \)
4050.1-a3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -4082\) , \( 14681\bigr] \)
4050.1-a4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -617\) , \( 5231\bigr] \)
4050.1-a5 \( \bigl[1\) , \( -1\) , \( 1\) , \( -167\) , \( -709\bigr] \)
4050.1-a6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -3002\) , \( 63929\bigr] \)
4050.1-a7 \( \bigl[1\) , \( -1\) , \( 1\) , \( -2597\) , \( -50281\bigr] \)
4050.1-a8 \( \bigl[1\) , \( -1\) , \( 1\) , \( -48002\) , \( 4059929\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph