Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-176.1-a
Conductor 176.1
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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 176.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 176.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
176.1-a1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \)
176.1-a2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph