Elliptic curve isogeny class 73.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-73.2-a
• Conductor: 73.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 73.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 73.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
73.2-a1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 14\) , \( 16 a - 6\bigr] \)
73.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -6 a - 1\) , \( 4 a\bigr] \)
73.2-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
73.2-a4	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -9 a + 14\) , \( 30 a - 24\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph