Elliptic curve isogeny class 576.5-i over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-576.5-i
• Conductor: 576.5
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 576.5-i over \(\Q(\sqrt{33}) \)

Isogeny class 576.5-i contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
576.5-i1	\( \bigl[a\) , \( a\) , \( a\) , \( 60 a + 139\) , \( -1013 a - 2404\bigr] \)
576.5-i2	\( \bigl[a\) , \( a\) , \( a\) , \( 774 a - 2603\) , \( -20627 a + 69566\bigr] \)