Elliptic curve isogeny class 147.1-b over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-147.1-b
• Conductor: 147.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 147.1-b over \(\Q(\sqrt{33}) \)

Isogeny class 147.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
147.1-b1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -12519 a - 29697\) , \( 3604391 a + 8550628\bigr] \)
147.1-b2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 361 a + 858\) , \( 1946 a + 4615\bigr] \)
147.1-b3	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 1480 a - 4987\) , \( -10461 a + 35272\bigr] \)
147.1-b4	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -14359 a - 34062\) , \( -1599934 a - 3795495\bigr] \)
147.1-b5	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -18039 a - 42792\) , \( 2204216 a + 5229019\bigr] \)
147.1-b6	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -288519 a - 684447\) , \( 142523801 a + 338106550\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph