Elliptic curve isogeny class 1536.1-k over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1536.1-k
• Conductor: 1536.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1536.1-k over \(\Q(\sqrt{3}) \)

Isogeny class 1536.1-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1536.1-k1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 8\) , \( -12 a + 20\bigr] \)
1536.1-k2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
1536.1-k3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 26 a - 47\) , \( -77 a + 135\bigr] \)
1536.1-k4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 6 a - 17\) , \( 23 a - 45\bigr] \)

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