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

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

Isogeny class 28672.7-w contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
28672.7-w1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -853 a + 1022\) , \( -809 a + 17334\bigr] \)
28672.7-w2	\( \bigl[0\) , \( a\) , \( 0\) , \( 159 a - 58\) , \( -491 a - 798\bigr] \)
28672.7-w3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -53 a + 62\) , \( -9 a + 246\bigr] \)
28672.7-w4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 85 a + 105\) , \( 169 a - 1299\bigr] \)
28672.7-w5	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 23\) , \( -105 a + 51\bigr] \)
28672.7-w6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 55\) , \( 41 a - 147\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 8 & 4 & 4 \\ 8 & 1 & 4 & 4 & 8 & 2 \\ 2 & 4 & 1 & 4 & 2 & 2 \\ 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 8 & 2 & 8 & 1 & 4 \\ 4 & 2 & 2 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph