Elliptic curve isogeny class 176.4-b over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-176.4-b
• Conductor: 176.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 176.4-b over \(\Q(\sqrt{33}) \)

Isogeny class 176.4-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
176.4-b1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 21 a + 49\) , \( 71 a + 168\bigr] \)
176.4-b2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 5 a + 1\) , \( 3 a + 12\bigr] \)
176.4-b3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 20 a - 54\) , \( 63 a - 208\bigr] \)
176.4-b4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -359 a + 1229\) , \( -1089 a + 3696\bigr] \)

Rank

Rank: \( 1 \)

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