Elliptic curve isogeny class 86016.1-bm over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-86016.1-bm
• Conductor: 86016.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 2 & 4 & 4 & 2 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 2 & 4 & 1 & 8 & 8 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 8 & 4 & 1 & 8 \\ 2 & 4 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 86016.1-bm over \(\Q(\sqrt{-3}) \)

Isogeny class 86016.1-bm contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
86016.1-bm1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 57 a - 68\) , \( 212 a - 157\bigr] \)
86016.1-bm2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3 a - 8\) , \( 8 a + 11\bigr] \)
86016.1-bm3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 137 a + 12\) , \( 388 a - 1181\bigr] \)
86016.1-bm4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -43 a + 52\) , \( 28 a + 135\bigr] \)
86016.1-bm5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -63 a - 128\) , \( 416 a + 575\bigr] \)
86016.1-bm6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 937 a - 1108\) , \( 14052 a - 9885\bigr] \)