Elliptic curve isogeny class 1152.1-o over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1152.1-o
• Conductor: 1152.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1152.1-o over \(\Q(\sqrt{3}) \)

Isogeny class 1152.1-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1152.1-o1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 9833 a - 17031\) , \( 219131 a - 379546\bigr] \)
1152.1-o2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1594 a - 2760\) , \( -44284 a + 76702\bigr] \)
1152.1-o3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 88598 a - 153456\) , \( -18917635 a + 32766305\bigr] \)
1152.1-o4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 15\) , \( -261 a + 450\bigr] \)