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

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

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

Curve label	Weierstrass Coefficients
28672.7-d1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 33\bigr] \)
28672.7-d2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 17 a - 39\) , \( -53 a + 55\bigr] \)
28672.7-d3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -15 a - 23\) , \( 69 a + 25\bigr] \)
28672.7-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -161\) , \( 833\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph