Elliptic curve isogeny class 171.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-171.1-a
• Conductor: 171.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 171.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 171.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
171.1-a1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a - 5\) , \( 9 a + 3\bigr] \)
171.1-a2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -20 a + 25\) , \( 18 a + 48\bigr] \)
171.1-a3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 0\) , \( -a\bigr] \)
171.1-a4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 5 a + 5\) , \( -11 a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph