Elliptic curve isogeny class 28672.7-q over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28672.7-q
• Conductor: 28672.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 28672.7-q over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.7-q contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
28672.7-q1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -127 a - 87\) , \( 1061 a - 135\bigr] \)
28672.7-q2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7 a + 9\) , \( 7 a - 11\bigr] \)
28672.7-q3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a - 7\) , \( 21 a - 7\bigr] \)
28672.7-q4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -16 a + 15\) , \( 16 a - 47\bigr] \)

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