Elliptic curve isogeny class 11.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-11.1-a
• Conductor: 11.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 11.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 11.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
11.1-a1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -2877883 a - 6827148\) , \( 4506151140 a + 10689858189\bigr] \)
11.1-a2	\( \bigl[0\) , \( a\) , \( 1\) , \( 3803 a - 12821\) , \( -394830 a + 1331479\bigr] \)
11.1-a3	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -123 a - 288\) , \( -2880 a - 6831\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph