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

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

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

Curve label	Weierstrass Coefficients
121.1-c1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -2641 a - 6272\) , \( -121729 a - 288772\bigr] \)
121.1-c2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -a - 2\) , \( 11 a + 26\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph