Elliptic curve isogeny class 110889.3-CMc over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-110889.3-CMc
• Conductor: 110889.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 110889.3-CMc over \(\Q(\sqrt{-3}) \)

Isogeny class 110889.3-CMc contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
110889.3-CMc1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 63 a - 18\bigr] \)
110889.3-CMc2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -990 a - 210\) , \( 15939 a - 4491\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph