Elliptic curve isogeny class 576.6-l over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-576.6-l
• Conductor: 576.6
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 576.6-l over \(\Q(\sqrt{33}) \)

Isogeny class 576.6-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.6-l1	\( \bigl[a\) , \( a\) , \( 0\) , \( 36 a - 108\) , \( -189 a + 648\bigr] \)
576.6-l2	\( \bigl[a\) , \( a\) , \( 0\) , \( -10471 a + 35324\) , \( 52022 a - 175424\bigr] \)
576.6-l3	\( \bigl[a\) , \( a\) , \( 0\) , \( 2624 a - 8836\) , \( 5243 a - 17672\bigr] \)
576.6-l4	\( \bigl[a\) , \( a\) , \( 0\) , \( -154 a - 367\) , \( 1484 a + 3520\bigr] \)