Elliptic curve isogeny class 43681.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43681.1-b
• Conductor: 43681.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 43681.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 43681.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
43681.1-b1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -10 a + 12\) , \( -4 a + 4\bigr] \)
43681.1-b2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -90 a + 117\) , \( -209 a - 291\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph