Elliptic curve isogeny class 111132.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-111132.3-a
• Conductor: 111132.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 111132.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 111132.3-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
111132.3-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -278 a + 356\) , \( 716 a + 1746\bigr] \)
111132.3-a2	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 23 a + 50\) , \( 225 a - 358\bigr] \)
111132.3-a3	\( \bigl[a\) , \( a\) , \( 0\) , \( -27 a - 45\) , \( 79 a - 293\bigr] \)
111132.3-a4	\( \bigl[a\) , \( a\) , \( 0\) , \( 178 a - 275\) , \( -1485 a + 1396\bigr] \)
111132.3-a5	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -778 a + 353\) , \( -5643 a + 7157\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph