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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-9216.7-a
• 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-a over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
9216.7-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a + 5\) , \( -9 a + 22\bigr] \)
9216.7-a2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a\) , \( 12 a - 4\bigr] \)
9216.7-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 1\) , \( -2 a - 16\bigr] \)
9216.7-a4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -128 a\) , \( 684 a - 484\bigr] \)

Rank

Rank: \( 1 \)

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