Elliptic curve isogeny class 54756.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54756.1-a
• Conductor: 54756.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 54756.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 54756.1-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
54756.1-a1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1161 a + 879\) , \( 5112 a - 14564\bigr] \)
54756.1-a2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -1131 a + 189\) , \( -14898 a + 10660\bigr] \)
54756.1-a3	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 47 a - 22\) , \( 86 a + 26\bigr] \)
54756.1-a4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 204 a - 96\) , \( 957 a + 388\bigr] \)
54756.1-a5	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -21 a + 9\) , \( -18 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 9 & 9 & 3 \\ 9 & 1 & 9 & 9 & 3 \\ 9 & 9 & 1 & 9 & 3 \\ 9 & 9 & 9 & 1 & 3 \\ 3 & 3 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph