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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54684.6-b
• Conductor: 54684.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 54684.6-b over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.6-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
54684.6-b1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 22958 a + 1487\) , \( -108899 a + 1456079\bigr] \)
54684.6-b2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 8 a - 13\) , \( a - 1\bigr] \)
54684.6-b3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -277 a + 2\) , \( -1046 a - 325\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph