Elliptic curve isogeny class 324.1-d over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-324.1-d
• Conductor: 324.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.1-d over \(\Q(\sqrt{33}) \)

Isogeny class 324.1-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
324.1-d1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1173 a - 2783\) , \( -37248 a - 88363\bigr] \)
324.1-d2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \)
324.1-d3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph