Elliptic curve isogeny class 9216.7-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9216.7-e
• Conductor: 9216.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 9216.7-e over \(\Q(\sqrt{-7}) \)

Isogeny class 9216.7-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.7-e1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3 a - 17\) , \( -2 a + 22\bigr] \)
9216.7-e2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -12 a + 8\) , \( 12 a - 20\bigr] \)
9216.7-e3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a + 1\) , \( 3 a + 2\bigr] \)
9216.7-e4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -18 a - 19\) , \( 63 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph