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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-539.1-e
• Conductor: 539.1
• Rank: \( 1 \)

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

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

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

Isogeny class 539.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
539.1-e1	\( \bigl[1\) , \( -a\) , \( a\) , \( 1280 a + 3040\) , \( -161701 a - 383601\bigr] \)
539.1-e2	\( \bigl[1\) , \( -a\) , \( a\) , \( -18960 a - 44975\) , \( -2203466 a - 5227242\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph