Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-99.1-b
Conductor 99.1
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 99.1-b over \(\Q(\sqrt{33}) \)

Isogeny class 99.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
99.1-b1 \( \bigl[1\) , \( -1\) , \( 1\) , \( 60 a + 142\) , \( -96 a - 228\bigr] \)
99.1-b2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -2\) , \( 0\bigr] \)
99.1-b3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -17\) , \( 30\bigr] \)
99.1-b4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -60 a + 202\) , \( 96 a - 324\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph