Elliptic curve isogeny class 52.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-52.1-a
• Conductor: 52.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 52.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 52.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
52.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2\) , \( -2 a + 3\bigr] \)
52.1-a2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 60 a - 98\) , \( -306 a + 527\bigr] \)
52.1-a3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 3 a - 53\) , \( -61 a + 76\bigr] \)
52.1-a4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -7 a - 13\) , \( -29 a - 50\bigr] \)

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