Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-36864.7-u
Conductor 36864.7
Rank \( 0 \)

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 36864.7-u over \(\Q(\sqrt{-7}) \)

Isogeny class 36864.7-u contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
36864.7-u1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 63\) , \( 1377\bigr] \)
36864.7-u2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -3\bigr] \)
36864.7-u3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( -15\bigr] \)
36864.7-u4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -97\) , \( 385\bigr] \)
36864.7-u5 \( \bigl[0\) , \( -1\) , \( 0\) , \( -257\) , \( -1503\bigr] \)
36864.7-u6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -1537\) , \( 23713\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph