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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28672.7-o
• Conductor: 28672.7
• Rank: \( 0 \)

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

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

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

Isogeny class 28672.7-o contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
28672.7-o1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -10913\) , \( -436447\bigr] \)
28672.7-o2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 641 a + 393\) , \( 3355 a - 15449\bigr] \)
28672.7-o3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -639 a + 1033\) , \( -2715 a - 13127\bigr] \)
28672.7-o4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( 165 a - 135\bigr] \)
28672.7-o5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 73\) , \( -165 a + 103\bigr] \)
28672.7-o6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 161\bigr] \)
28672.7-o7	\( \bigl[0\) , \( -1\) , \( 0\) , \( 287\) , \( -3231\bigr] \)
28672.7-o8	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1919 a - 567\) , \( 13275 a - 80665\bigr] \)
28672.7-o9	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1921 a - 2487\) , \( -15195 a - 64903\bigr] \)
28672.7-o10	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2273\) , \( -33439\bigr] \)
28672.7-o11	\( \bigl[0\) , \( -1\) , \( 0\) , \( -673\) , \( 6945\bigr] \)
28672.7-o12	\( \bigl[0\) , \( -1\) , \( 0\) , \( -174753\) , \( -28059871\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph