Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-16562.2-e
Conductor 16562.2
Rank \( 1 \)

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 16562.2-e over \(\Q(\sqrt{-1}) \)

Isogeny class 16562.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
16562.2-e1 \( \bigl[i\) , \( 1\) , \( i\) , \( 867\) , \( -6445\bigr] \)
16562.2-e2 \( \bigl[i\) , \( 1\) , \( i\) , \( -4253\) , \( -59693\bigr] \)
16562.2-e3 \( \bigl[i\) , \( 1\) , \( i\) , \( -31293\) , \( 2081875\bigr] \)
16562.2-e4 \( \bigl[i\) , \( 1\) , \( i\) , \( -59133\) , \( -5547693\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph