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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-33.2-c
• 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-c over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
33.2-c1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
33.2-c2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 25 a - 29\) , \( 89 a - 138\bigr] \)
33.2-c3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 20 a - 39\) , \( 84 a - 138\bigr] \)
33.2-c4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 335 a - 609\) , \( 4719 a - 8214\bigr] \)
33.2-c5	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( 4 a + 1\bigr] \)
33.2-c6	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -20 a - 49\) , \( 100 a + 184\bigr] \)

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