Elliptic curve isogeny class 512.4-l over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-512.4-l
• Conductor: 512.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 512.4-l over \(\Q(\sqrt{33}) \)

Isogeny class 512.4-l contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
512.4-l1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 60 a - 200\) , \( -492 a + 1660\bigr] \)
512.4-l2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -17 a - 40\) , \( -17 a - 40\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph