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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-121.1-a
• 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-a over \(\Q(\sqrt{33}) \)

Isogeny class 121.1-a contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
121.1-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -11048 a - 26206\) , \( 1082764 a + 2568621\bigr] \)
121.1-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( -7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph