Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-33.1-b
Conductor 33.1
Rank not recorded

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-b over \(\Q(\sqrt{33}) \)

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

Curve label Weierstrass Coefficients
33.1-b1 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a - 1\) , \( 9 a + 24\bigr] \)
33.1-b2 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16001 a + 53960\) , \( 639500 a - 2156578\bigr] \)
33.1-b3 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 4239 a - 14295\) , \( 75585 a - 254898\bigr] \)
33.1-b4 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2399 a - 8090\) , \( -110030 a + 371048\bigr] \)
33.1-b5 \( \bigl[1\) , \( -a\) , \( a\) , \( -53920 a - 127910\) , \( -11482951 a - 27240791\bigr] \)
33.1-b6 \( \bigl[1\) , \( -a\) , \( a\) , \( -1\) , \( -10 a + 34\bigr] \)

Rank

Rank not yet determined.

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