Elliptic curve isogeny class 176.1-b over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-176.1-b
• Conductor: 176.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 176.1-b over \(\Q(\sqrt{33}) \)

Isogeny class 176.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
176.1-b1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 28459 a - 95968\) , \( -4431843 a + 14945420\bigr] \)
176.1-b2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -981 a + 3312\) , \( -33363 a + 112508\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph