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

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

Isogeny class 33.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
33.2-a1	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 6 a - 5\) , \( -3 a + 8\bigr] \)
33.2-a2	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 460938 a - 798369\) , \( -223745835 a + 387539154\bigr] \)
33.2-a3	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 8273 a - 14331\) , \( -535987 a + 928356\bigr] \)
33.2-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -7 a - 8\) , \( -12 a - 19\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph