Elliptic curve isogeny class 54684.2-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.2-e
• Conductor: 54684.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 54684.2-e over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.2-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
54684.2-e1	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -228 a + 108\) , \( 635 a - 1797\bigr] \)
54684.2-e2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -4068 a + 2508\) , \( 51707 a - 92517\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph