Elliptic curve isogeny class 138384.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-138384.2-b
• Conductor: 138384.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 138384.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 138384.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
138384.2-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 36 a - 33\) , \( -84 a + 37\bigr] \)
138384.2-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -36 a + 3\) , \( 84 a - 47\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph