Elliptic curve isogeny class 54684.1-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.1-d
• Conductor: 54684.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 54684.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.1-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
54684.1-d1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -276 a - 3\) , \( 770 a - 1373\bigr] \)
54684.1-d2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6 a + 12\) , \( -7 a + 13\bigr] \)
54684.1-d3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 24444 a - 1488\) , \( 133343 a + 1345693\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph