Elliptic curve isogeny class 33.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-33.1-b
• Conductor: 33.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 33.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 33.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
33.1-b1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -727 a + 1262\) , \( 19515 a - 33800\bigr] \)
33.1-b2	\( \bigl[1\) , \( 0\) , \( a\) , \( 3362 a - 5824\) , \( 177111 a - 306766\bigr] \)
33.1-b3	\( \bigl[1\) , \( -a\) , \( 0\) , \( 20 a - 49\) , \( 100 a - 184\bigr] \)
33.1-b4	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 298 a - 513\) , \( 3675 a - 6364\bigr] \)
33.1-b5	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 318 a - 548\) , \( 3150 a - 5455\bigr] \)
33.1-b6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1683 a - 2918\) , \( -46815 a + 81086\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph