Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-539.1-f
Conductor 539.1
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 539.1-f over \(\Q(\sqrt{33}) \)

Isogeny class 539.1-f contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
539.1-f1 \( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \)
539.1-f2 \( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \)
539.1-f3 \( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph