Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-196.1-a
Conductor 196.1
Rank not recorded

Related objects

Learn more about

Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 196.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 196.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
196.1-a1 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -62751 a - 148862\) , \( 14446740 a + 34271731\bigr] \)
196.1-a2 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 192 a - 644\) , \( 5057 a - 17061\bigr] \)
196.1-a3 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -1648 a + 5561\) , \( -104508 a + 352423\bigr] \)
196.1-a4 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 13072 a - 44079\) , \( -1123028 a + 3787159\bigr] \)
196.1-a5 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -3871 a - 9182\) , \( -228060 a - 541023\bigr] \)
196.1-a6 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -1004831 a - 2383742\) , \( 927667860 a + 2200689139\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph