Elliptic curve isogeny class 588.1-n over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-588.1-n
• Conductor: 588.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 588.1-n over \(\Q(\sqrt{33}) \)

Isogeny class 588.1-n contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
588.1-n1	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 11 a - 39\) , \( 36 a - 126\bigr] \)
588.1-n2	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -109 a - 258\) , \( -763 a - 1810\bigr] \)
588.1-n3	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -29 a - 68\) , \( 177 a + 420\bigr] \)
588.1-n4	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -95 a + 326\) , \( 2639 a - 8902\bigr] \)