Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 1.1-a contains 6 curves linked by isogenies of degrees dividing 99.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[0\) , \( -a\) , \( 1\) , \( -435 a - 1030\) , \( -7890 a - 18717\bigr] \)
1.1-a2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -25 a + 85\) , \( 72 a - 243\bigr] \)
1.1-a3	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 5 a - 15\) , \( 6 a - 20\bigr] \)
1.1-a4	\( \bigl[0\) , \( -a\) , \( 1\) , \( -5 a - 10\) , \( -6 a - 14\bigr] \)
1.1-a5	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 435 a - 1465\) , \( 7890 a - 26607\bigr] \)
1.1-a6	\( \bigl[0\) , \( -a\) , \( 1\) , \( 25 a + 60\) , \( -72 a - 171\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 99 & 33 & 3 & 11 & 9 \\ 99 & 1 & 3 & 33 & 9 & 11 \\ 33 & 3 & 1 & 11 & 3 & 33 \\ 3 & 33 & 11 & 1 & 33 & 3 \\ 11 & 9 & 3 & 33 & 1 & 99 \\ 9 & 11 & 33 & 3 & 99 & 1 \end{array}\right)\)

Isogeny graph