Elliptic curve isogeny class 81.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-81.1-a
• Conductor: 81.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 81.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 81.1-a contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
81.1-a1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -11040 a - 26190\) , \( -1070190 a - 2538792\bigr] \)
81.1-a2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -30\) , \( 63\bigr] \)
81.1-a3	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 4230 a - 14265\bigr] \)
81.1-a4	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph