Elliptic curve isogeny class 9984.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9984.1-a
• Conductor: 9984.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 9984.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 9984.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9984.1-a1	\( \bigl[0\) , \( a\) , \( 0\) , \( -16 a - 48\) , \( -92 a - 116\bigr] \)
9984.1-a2	\( \bigl[0\) , \( a\) , \( 0\) , \( -21 a + 2\) , \( 35 a - 21\bigr] \)
9984.1-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a - 3\) , \( -11 a - 14\bigr] \)
9984.1-a4	\( \bigl[0\) , \( a\) , \( 0\) , \( -a - 3\) , \( -2 a - 2\bigr] \)