Elliptic curve isogeny class 4096.1-CMa over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-4096.1-CMa
• Conductor: 4096.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4096.1-CMa over \(\Q(\sqrt{-3}) \)

Isogeny class 4096.1-CMa contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4096.1-CMa1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -2 a + 1\bigr] \)
4096.1-CMa2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 21 a - 20\) , \( -46 a + 33\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph