Elliptic curve isogeny class 273.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-273.2-a
• Conductor: 273.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 273.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 273.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
273.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 64 a + 15\) , \( 102 a - 313\bigr] \)
273.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24 a - 15\) , \( 36 a - 9\bigr] \)
273.2-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \)
273.2-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 4 a\) , \( 3 a - 7\bigr] \)
273.2-a5	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 59 a + 85\) , \( -405 a + 86\bigr] \)
273.2-a6	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -26 a - 10\) , \( -85 a + 29\bigr] \)
273.2-a7	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -26 a - 15\) , \( -78 a + 47\bigr] \)
273.2-a8	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -111 a - 195\) , \( 837 a + 1080\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 4 & 2 & 3 & 12 & 6 & 12 \\ 4 & 1 & 4 & 2 & 12 & 12 & 6 & 3 \\ 4 & 4 & 1 & 2 & 12 & 3 & 6 & 12 \\ 2 & 2 & 2 & 1 & 6 & 6 & 3 & 6 \\ 3 & 12 & 12 & 6 & 1 & 4 & 2 & 4 \\ 12 & 12 & 3 & 6 & 4 & 1 & 2 & 4 \\ 6 & 6 & 6 & 3 & 2 & 2 & 1 & 2 \\ 12 & 3 & 12 & 6 & 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph