Elliptic curve isogeny class 64.7-g over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-64.7-g
• Conductor: 64.7
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 64.7-g over \(\Q(\sqrt{33}) \)

Isogeny class 64.7-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
64.7-g1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 7 a - 16\) , \( -8 a + 31\bigr] \)
64.7-g2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -618 a - 1466\) , \( 4553 a + 10801\bigr] \)
64.7-g3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a - 12\) , \( -24 a - 57\bigr] \)
64.7-g4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -100 a - 237\) , \( -1101 a - 2612\bigr] \)