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

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-288.3-b
• Conductor: 288.3
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
288.3-b1	\( \bigl[a\) , \( a\) , \( 0\) , \( 733 a - 2459\) , \( -18172 a + 61290\bigr] \)
288.3-b2	\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 5\) , \( -a + 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph