Elliptic curve isogeny class 5776.3-CMb over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-5776.3-CMb
• Conductor: 5776.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 5776.3-CMb over \(\Q(\sqrt{-3}) \)

Isogeny class 5776.3-CMb contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
5776.3-CMb1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 6 a - 18\bigr] \)
5776.3-CMb2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a + 80\) , \( 180 a - 460\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph