Elliptic curve isogeny class 9216.5-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9216.5-e
• Conductor: 9216.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 9216.5-e over \(\Q(\sqrt{-7}) \)

Isogeny class 9216.5-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9216.5-e1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 32\) , \( 180 a + 360\bigr] \)
9216.5-e2	\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
9216.5-e3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -4 a + 8\) , \( -4 a - 8\bigr] \)
9216.5-e4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -24 a + 48\) , \( 36 a + 72\bigr] \)
9216.5-e5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -64 a + 128\) , \( -220 a - 440\bigr] \)
9216.5-e6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -384 a + 768\) , \( 2772 a + 5544\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph