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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.6-c
• 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-c over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
54684.6-c1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 418 a - 359\) , \( -3201 a + 750\bigr] \)
54684.6-c2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 28 a - 29\) , \( -27 a - 36\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph