Elliptic curve isogeny class 539.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-539.1-a
• Conductor: 539.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 539.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 539.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
539.1-a1	\( \bigl[0\) , \( -a\) , \( 1\) , \( 32875 a - 110860\) , \( 5524839 a - 18631313\bigr] \)
539.1-a2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -18155 a - 43065\) , \( -10448199 a - 24786069\bigr] \)
539.1-a3	\( \bigl[0\) , \( -a\) , \( 1\) , \( -162165 a + 546870\) , \( -270199791 a + 911189707\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph