Elliptic curve isogeny class 54684.5-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.5-d
• Conductor: 54684.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 54684.5-d over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.5-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
54684.5-d1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -312 a + 219\) , \( -476 a - 759\bigr] \)
54684.5-d2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 3 a + 9\) , \( 7 a - 3\bigr] \)
54684.5-d3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 26253 a - 19941\) , \( 1517257 a - 275523\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 5 \\ 5 & 1 & 25 \\ 5 & 25 & 1 \end{array}\right)\)

Isogeny graph