Elliptic curve isogeny class 128772.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-128772.3-e
• Conductor: 128772.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 128772.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 128772.3-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
128772.3-e1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 198 a - 3\) , \( -141 a - 996\bigr] \)
128772.3-e2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -17 a - 567\) , \( -2142 a - 1960\bigr] \)
128772.3-e3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 168 a + 567\) , \( -8379 a + 5292\bigr] \)
128772.3-e4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 103 a - 327\) , \( -942 a + 2120\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph