Elliptic curve isogeny class 43264.1-CMe over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43264.1-CMe
• Conductor: 43264.1
• Rank bounds: 0...2

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

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

Rank

Rank \(r\) satisfies \(0 \le r \le 2\)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 43264.1-CMe over \(\Q(\sqrt{-3}) \)

Isogeny class 43264.1-CMe contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
43264.1-CMe1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -8 a + 10\bigr] \)
43264.1-CMe2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 41 a - 75\) , \( -173 a + 256\bigr] \)