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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9984.1-c
• Conductor: 9984.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

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-c over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
9984.1-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -16 a - 48\) , \( 92 a + 116\bigr] \)
9984.1-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a + 2\) , \( -35 a + 21\bigr] \)
9984.1-c3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 3\) , \( 11 a + 14\bigr] \)
9984.1-c4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 3\) , \( 2 a + 2\bigr] \)