Elliptic curve isogeny class 1156.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-1156.1-a
• Conductor: 1156.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1156.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 1156.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1156.1-a1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3 a + 3\) , \( 1\bigr] \)
1156.1-a2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -113 a + 113\) , \( -329\bigr] \)
1156.1-a3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -43 a + 43\) , \( 105\bigr] \)
1156.1-a4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -103 a + 103\) , \( -411\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph