Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-28224.1-b
Conductor 28224.1
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 28224.1-b over \(\Q(\sqrt{-1}) \)

Isogeny class 28224.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
28224.1-b1 \( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 4\) , \( -11 i\bigr] \)
28224.1-b2 \( \bigl[0\) , \( -i\) , \( 0\) , \( 12\) , \( -18 i\bigr] \)
28224.1-b3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -14\) , \( -24\bigr] \)
28224.1-b4 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 56\) , \( -171 i\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph