Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-33.1-a
Conductor 33.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 33.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 33.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
33.1-a1 \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 943 a - 3179\) , \( 27552 a - 92919\bigr] \)
33.1-a2 \( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
33.1-a3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
33.1-a4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
33.1-a5 \( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)
33.1-a6 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -944 a - 2235\) , \( -27553 a - 65366\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph