Elliptic curve isogeny class 33.2-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-33.2-b
• Conductor: 33.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 33.2-b over \(\Q(\sqrt{3}) \)

Isogeny class 33.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
33.2-b1	\( \bigl[1\) , \( a\) , \( 0\) , \( 1\) , \( 0\bigr] \)
33.2-b2	\( \bigl[1\) , \( a\) , \( 0\) , \( 25 a - 29\) , \( -89 a + 138\bigr] \)
33.2-b3	\( \bigl[1\) , \( a\) , \( 0\) , \( 20 a - 39\) , \( -84 a + 138\bigr] \)
33.2-b4	\( \bigl[1\) , \( a\) , \( 0\) , \( 335 a - 609\) , \( -4719 a + 8214\bigr] \)
33.2-b5	\( \bigl[1\) , \( a\) , \( 0\) , \( -4\) , \( -4 a - 1\bigr] \)
33.2-b6	\( \bigl[1\) , \( a\) , \( 0\) , \( -20 a - 49\) , \( -100 a - 184\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph