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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1536.1-c
• Conductor: 1536.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1536.1-c1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 34114 a - 59087\) , \( -4482861 a + 7764543\bigr] \)
1536.1-c2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2149 a - 3722\) , \( -67356 a + 116664\bigr] \)
1536.1-c3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -706 a + 1223\) , \( -240609 a + 416747\bigr] \)
1536.1-c4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 26 a - 49\) , \( 74 a - 133\bigr] \)

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