Elliptic curve isogeny class 4.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-4.1-a
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 4.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -746 a - 1771\) , \( 18744 a + 44466\bigr] \)
4.1-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -36 a - 86\) , \( -2492 a - 5912\bigr] \)
4.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 4 a + 9\) , \( 92 a + 218\bigr] \)
4.1-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -4 a + 13\) , \( -92 a + 310\bigr] \)
4.1-a5	\( \bigl[1\) , \( 0\) , \( 1\) , \( 36 a - 122\) , \( 2492 a - 8404\bigr] \)
4.1-a6	\( \bigl[1\) , \( 0\) , \( 1\) , \( 746 a - 2517\) , \( -18744 a + 63210\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph