Elliptic curve isogeny class 288.3-o over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-288.3-o
• Conductor: 288.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 288.3-o over \(\Q(\sqrt{33}) \)

Isogeny class 288.3-o contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
288.3-o1	\( \bigl[a\) , \( a\) , \( a\) , \( 4 a + 5\) , \( 5 a + 10\bigr] \)
288.3-o2	\( \bigl[a\) , \( a\) , \( a\) , \( -415 a - 987\) , \( -2231 a - 5294\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph