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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-132.1-g
• 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-g over \(\Q(\sqrt{33}) \)

Isogeny class 132.1-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
132.1-g1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -4424 a - 10492\) , \( 1287370 a + 3054004\bigr] \)
132.1-g2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 3 a + 11\) , \( 3 a + 5\bigr] \)
132.1-g3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -744 a - 1762\) , \( 440 a + 1044\bigr] \)
132.1-g4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 8103 a - 27325\) , \( -679261 a + 2290657\bigr] \)
132.1-g5	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -4 a + 14\) , \( -4 a + 8\bigr] \)
132.1-g6	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 129543 a - 436855\) , \( -43147951 a + 145507027\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph