Elliptic curve isogeny class 52.2-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-52.2-a
• Conductor: 52.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 52.2-a over \(\Q(\sqrt{3}) \)

Isogeny class 52.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
52.2-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -192 a + 334\) , \( -730 a + 1265\bigr] \)
52.2-a2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 28 a - 46\) , \( 126 a - 219\bigr] \)
52.2-a3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10 a - 11\) , \( 16 a - 25\bigr] \)
52.2-a4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -51\) , \( 8 a + 71\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph