Elliptic curve isogeny class 111132.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-111132.2-a
• Conductor: 111132.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 111132.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 111132.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
111132.2-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 73 a - 49\) , \( -226 a - 132\bigr] \)
111132.2-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -72 a + 45\) , \( -79 a - 214\bigr] \)
111132.2-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -97 a + 275\) , \( 1485 a - 89\bigr] \)
111132.2-a4	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 77 a - 355\) , \( -717 a + 2462\bigr] \)
111132.2-a5	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -351 a + 777\) , \( 6069 a + 1866\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 3 & 3 & 3 \\ 3 & 1 & 9 & 9 & 9 \\ 3 & 9 & 1 & 9 & 9 \\ 3 & 9 & 9 & 1 & 9 \\ 3 & 9 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph