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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-132.1-a
• Conductor: 132.1
• Rank: \( 1 \)

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

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

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

Isogeny class 132.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
132.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \)
132.1-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \)
132.1-a3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 11664 a - 39329\) , \( 1157653 a - 3903931\bigr] \)
132.1-a4	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -153 a - 361\) , \( -1165 a - 2765\bigr] \)
132.1-a5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \)
132.1-a6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \)
132.1-a7	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 154 a - 514\) , \( 1318 a - 4444\bigr] \)
132.1-a8	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -11663 a - 27666\) , \( -1145990 a - 2718612\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph