Elliptic curve isogeny class 273.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-273.3-a
• Conductor: 273.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 273.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 273.3-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
273.3-a1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -64 a + 80\) , \( -87 a - 147\bigr] \)
273.3-a2	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -24 a + 10\) , \( -51 a + 51\bigr] \)
273.3-a3	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( a\) , \( -1\bigr] \)
273.3-a4	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -4 a + 5\) , \( -3 a\bigr] \)
273.3-a5	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -59 a + 145\) , \( 490 a - 260\bigr] \)
273.3-a6	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 26 a - 35\) , \( 75 a - 82\bigr] \)
273.3-a7	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 26 a - 40\) , \( 63 a - 57\bigr] \)
273.3-a8	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 111 a - 305\) , \( -1032 a + 1806\bigr] \)

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