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

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

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
9216.1-e1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 32\) , \( -20 a + 60\bigr] \)
9216.1-e2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 2\) , \( 4 a\bigr] \)
9216.1-e3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -11 a + 28\) , \( 46 a + 15\bigr] \)
9216.1-e4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 64 a - 32\) , \( 160 a + 12\bigr] \)