Elliptic curve isogeny class 99.1-a over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-99.1-a
• Conductor: 99.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 99.1-a over \(\Q(\sqrt{33}) \)

Isogeny class 99.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
99.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 9 a - 30\) , \( -27 a + 91\bigr] \)
99.1-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -621 a - 1473\) , \( 2799 a + 6640\bigr] \)
99.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 6141 a - 20709\) , \( 439971 a - 1483706\bigr] \)
99.1-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -9 a - 21\) , \( 27 a + 64\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph