Properties

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

Related objects

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

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

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

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

Curve label Weierstrass Coefficients
28672.7-e1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -10913\) , \( 436447\bigr] \)
28672.7-e2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 641 a + 393\) , \( -3355 a + 15449\bigr] \)
28672.7-e3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -639 a + 1033\) , \( 2715 a + 13127\bigr] \)
28672.7-e4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 73\) , \( -165 a + 135\bigr] \)
28672.7-e5 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 73\) , \( 165 a - 103\bigr] \)
28672.7-e6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -161\bigr] \)
28672.7-e7 \( \bigl[0\) , \( 1\) , \( 0\) , \( 287\) , \( 3231\bigr] \)
28672.7-e8 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1919 a - 567\) , \( -13275 a + 80665\bigr] \)
28672.7-e9 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1921 a - 2487\) , \( 15195 a + 64903\bigr] \)
28672.7-e10 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2273\) , \( 33439\bigr] \)
28672.7-e11 \( \bigl[0\) , \( 1\) , \( 0\) , \( -673\) , \( -6945\bigr] \)
28672.7-e12 \( \bigl[0\) , \( 1\) , \( 0\) , \( -174753\) , \( 28059871\bigr] \)

Rank

Rank: \( 1 \)

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