Elliptic curve isogeny class 576.7-l over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-576.7-l
• Conductor: 576.7
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 576.7-l over \(\Q(\sqrt{33}) \)

Isogeny class 576.7-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.7-l1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10478 a + 24857\) , \( -16697 a - 39610\bigr] \)
576.7-l2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -2617 a - 6208\) , \( -14078 a - 33397\bigr] \)
576.7-l3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -29 a - 68\) , \( 82 a + 195\bigr] \)
576.7-l4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 161 a - 517\) , \( -1850 a + 6260\bigr] \)