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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9216.1-b
• Conductor: 9216.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
9216.1-b1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -22 a + 23\) , \( -25 a + 1\bigr] \)
9216.1-b2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8 a - 7\) , \( -7 a + 7\bigr] \)
9216.1-b3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 53 a - 52\) , \( 146 a - 47\bigr] \)
9216.1-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 98 a - 97\) , \( -457 a + 277\bigr] \)

Rank

Rank: \( 0 \)

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