Elliptic curve isogeny class 54684.6-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.6-a
• Conductor: 54684.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 54684.6-a over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.6-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
54684.6-a1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 361 a + 223\) , \( -2381 a + 5031\bigr] \)
54684.6-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( a + 43\) , \( 103 a + 99\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph