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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.2-d
• 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-d over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.2-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
54684.2-d1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 19941 a - 26254\) , \( -1517258 a + 1241735\bigr] \)
54684.2-d2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -9 a - 4\) , \( -8 a + 5\bigr] \)
54684.2-d3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -219 a + 311\) , \( 475 a - 1234\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph