Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-192.1-c
Conductor 192.1
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 192.1-c over \(\Q(\sqrt{33}) \)

Isogeny class 192.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
192.1-c1 \( \bigl[0\) , \( a\) , \( 0\) , \( -5765 a + 19445\) , \( -2952054 a + 9955158\bigr] \)
192.1-c2 \( \bigl[0\) , \( a\) , \( 0\) , \( -245 a + 830\) , \( 4581 a - 15447\bigr] \)
192.1-c3 \( \bigl[0\) , \( a\) , \( 0\) , \( 1595 a - 5375\) , \( 42606 a - 143678\bigr] \)
192.1-c4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8955 a - 21240\) , \( 752814 a + 1785888\bigr] \)
192.1-c5 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -23675 a - 56160\) , \( -3341466 a - 7926896\bigr] \)
192.1-c6 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -141435 a - 335520\) , \( 49181094 a + 116671392\bigr] \)

Rank

Rank: \( 0 \)

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