Elliptic curve isogeny class 147456.1-ba over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-147456.1-ba
• Conductor: 147456.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 147456.1-ba over \(\Q(\sqrt{-3}) \)

Isogeny class 147456.1-ba contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
147456.1-ba1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 45 a + 12\) , \( -30 a + 105\bigr] \)
147456.1-ba2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 15 a + 12\) , \( 18 a - 45\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph