Elliptic curve isogeny class 396.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-396.1-a
• Conductor: 396.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 396.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 396.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
396.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -270 a - 642\) , \( 46800 a + 111024\bigr] \)
396.1-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 75 a - 252\) , \( -435 a + 1464\bigr] \)
396.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -147\) , \( -135\bigr] \)
396.1-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -75 a - 177\) , \( 435 a + 1029\bigr] \)
396.1-a5	\( \bigl[1\) , \( -1\) , \( 0\) , \( 23805 a - 80277\) , \( 3261195 a - 10997667\bigr] \)
396.1-a6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -87\) , \( 333\bigr] \)
396.1-a7	\( \bigl[1\) , \( -1\) , \( 0\) , \( -377085 a - 894552\) , \( -213522315 a - 506535000\bigr] \)
396.1-a8	\( \bigl[1\) , \( -1\) , \( 0\) , \( 270 a - 912\) , \( -46800 a + 157824\bigr] \)

Rank

Rank: \( 0 \)

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