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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1152.1-c
• Conductor: 1152.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1152.1-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 15\) , \( -13 a + 22\bigr] \)
1152.1-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a - 12\) , \( 12 a + 18\bigr] \)
1152.1-c3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 39 a - 74\) , \( 174 a - 306\bigr] \)
1152.1-c4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6 a + 1\) , \( 15 a - 24\bigr] \)

Rank

Rank: \( 1 \)

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