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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-121.1-f
• Conductor: 121.1
• Rank: \( 0 \)

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

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

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

Isogeny class 121.1-f contains 4 curves linked by isogenies of degrees dividing 22.

Curve label	Weierstrass Coefficients
121.1-f1	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -7001 a - 16608\) , \( -541087 a - 1283611\bigr] \)
121.1-f2	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 32 a - 106\) , \( 184 a - 613\bigr] \)
121.1-f3	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 1380 a - 4656\) , \( 83690 a - 282231\bigr] \)
121.1-f4	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -130 a - 327\) , \( -1652 a - 3880\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 11 & 22 & 2 \\ 11 & 1 & 2 & 22 \\ 22 & 2 & 1 & 11 \\ 2 & 22 & 11 & 1 \end{array}\right)\)

Isogeny graph