Elliptic curve isogeny class 121.1-b over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-121.1-b
• Conductor: 121.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 121.1-b over \(\Q(\sqrt{33}) \)

Isogeny class 121.1-b contains 6 curves linked by isogenies of degrees dividing 99.

Curve label	Weierstrass Coefficients
121.1-b1	\( \bigl[0\) , \( -1\) , \( 1\) , \( -110 a - 227\) , \( 1012 a + 2419\bigr] \)
121.1-b2	\( \bigl[0\) , \( a\) , \( 1\) , \( -12371 a + 41722\) , \( 513055 a - 1730165\bigr] \)
121.1-b3	\( \bigl[0\) , \( -1\) , \( 1\) , \( -7\) , \( 10\bigr] \)
121.1-b4	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2699 a - 6399\) , \( -130563 a - 309731\bigr] \)
121.1-b5	\( \bigl[0\) , \( -1\) , \( 1\) , \( 110 a - 337\) , \( -1012 a + 3431\bigr] \)
121.1-b6	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 12371 a + 29351\) , \( -513055 a - 1217110\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 99 & 3 & 33 & 9 & 11 \\ 99 & 1 & 33 & 3 & 11 & 9 \\ 3 & 33 & 1 & 11 & 3 & 33 \\ 33 & 3 & 11 & 1 & 33 & 3 \\ 9 & 11 & 3 & 33 & 1 & 99 \\ 11 & 9 & 33 & 3 & 99 & 1 \end{array}\right)\)

Isogeny graph