Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-36864.1-a
Conductor 36864.1
Rank \( 2 \)

Related objects

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Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 36864.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 36864.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
36864.1-a1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -159\) , \( -765\bigr] \)
36864.1-a2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( -3\bigr] \)
36864.1-a3 \( \bigl[0\) , \( -i\) , \( 0\) , \( 7\) , \( 5 i\bigr] \)
36864.1-a4 \( \bigl[0\) , \( i\) , \( 0\) , \( 647\) , \( 6555 i\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph