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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-4.1-b
• 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-b over \(\Q(\sqrt{33}) \)

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

Curve label	Weierstrass Coefficients
4.1-b1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 294 a - 990\) , \( 4809 a - 16223\bigr] \)
4.1-b2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 44 a - 145\) , \( -242 a + 809\bigr] \)
4.1-b3	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 4 a - 10\) , \( 7 a - 31\bigr] \)
4.1-b4	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -3 a - 6\) , \( -12 a - 29\bigr] \)
4.1-b5	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -43 a - 101\) , \( 197 a + 467\bigr] \)
4.1-b6	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -293 a - 696\) , \( -5104 a - 12109\bigr] \)

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