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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28672.7-x
• 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-x over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
28672.7-x1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a + 9\) , \( 119 a - 173\bigr] \)
28672.7-x2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3 a + 9\) , \( 7 a + 3\bigr] \)
28672.7-x3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 1\) , \( a + 3\bigr] \)
28672.7-x4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -43 a + 169\) , \( 439 a + 179\bigr] \)

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