Elliptic curve isogeny class 441.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-441.2-a
• Conductor: 441.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 441.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 441.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
441.2-a1	\( \bigl[1\) , \( -1\) , \( a\) , \( -26 a + 12\) , \( 161 a - 50\bigr] \)
441.2-a2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 25 a - 14\) , \( -162 a + 111\bigr] \)
441.2-a3	\( \bigl[1\) , \( -1\) , \( a\) , \( 4 a - 3\) , \( -4 a + 1\bigr] \)
441.2-a4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5 a + 1\) , \( 3 a - 3\bigr] \)
441.2-a5	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -20 a + 1\) , \( -30 a + 18\bigr] \)
441.2-a6	\( \bigl[1\) , \( -1\) , \( a\) , \( 19 a - 18\) , \( 29 a - 11\bigr] \)
441.2-a7	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -305 a + 16\) , \( -2190 a + 1269\bigr] \)
441.2-a8	\( \bigl[1\) , \( -1\) , \( a\) , \( 304 a - 288\) , \( 2189 a - 920\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph