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

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

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

Curve label	Weierstrass Coefficients
121.1-d1	\( \bigl[1\) , \( -a\) , \( a\) , \( -1643 a - 4079\) , \( 64852 a + 154652\bigr] \)
121.1-d2	\( \bigl[1\) , \( -a\) , \( a\) , \( -3 a - 4\) , \( -5 a - 13\bigr] \)
121.1-d3	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 2 a - 7\) , \( 4 a - 18\bigr] \)
121.1-d4	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 1642 a - 5722\) , \( -64853 a + 219504\bigr] \)

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