Elliptic curve isogeny class 128772.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-128772.2-c
• Conductor: 128772.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 128772.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 128772.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
128772.2-c1	\( \bigl[a\) , \( -1\) , \( 1\) , \( -543 a - 154\) , \( -6567 a + 1550\bigr] \)
128772.2-c2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -101 a + 136\) , \( 249 a - 604\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph