Elliptic curve isogeny class 9216.6-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9216.6-d
• Conductor: 9216.6
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 9216.6-d over \(\Q(\sqrt{-7}) \)

Isogeny class 9216.6-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.6-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \)
9216.6-d2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
9216.6-d3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \)
9216.6-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \)

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