Elliptic curve isogeny class 132.1-d over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-132.1-d
• Conductor: 132.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 132.1-d over \(\Q(\sqrt{33}) \)

Isogeny class 132.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
132.1-d1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \)
132.1-d2	\( \bigl[1\) , \( -a\) , \( a\) , \( 203 a - 683\) , \( -2490 a + 8393\bigr] \)
132.1-d3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \)
132.1-d4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \)
132.1-d5	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -204 a - 480\) , \( 2489 a + 5903\bigr] \)
132.1-d6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph