Elliptic curve isogeny class 9216.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9216.1-c
• Conductor: 9216.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 9216.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 9216.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.1-c1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 29\) , \( 23 a - 92\bigr] \)
9216.1-c2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 1\) , \( -a - 2\bigr] \)
9216.1-c3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 29 a - 16\) , \( -58 a + 13\bigr] \)
9216.1-c4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a - 31\) , \( -97 a - 44\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph