Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-121.1-h
Conductor 121.1
Rank \( 0 \)

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 121.1-h over \(\Q(\sqrt{33}) \)

Isogeny class 121.1-h contains 4 curves linked by isogenies of degrees dividing 22.

Curve label Weierstrass Coefficients
121.1-h1 \( \bigl[1\) , \( 1\) , \( 0\) , \( 68013 a - 229363\) , \( 16391683 a - 55277372\bigr] \)
121.1-h2 \( \bigl[1\) , \( 1\) , \( 0\) , \( 133 a - 448\) , \( -1359 a + 4583\bigr] \)
121.1-h3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -133 a - 315\) , \( 1359 a + 3224\bigr] \)
121.1-h4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -68013 a - 161350\) , \( -16391683 a - 38885689\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 11 & 22 & 2 \\ 11 & 1 & 2 & 22 \\ 22 & 2 & 1 & 11 \\ 2 & 22 & 11 & 1 \end{array}\right)\)

Isogeny graph