Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-54450.2-i
Conductor 54450.2
Rank \( 0 \)

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

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

Elliptic curves in class 54450.2-i over \(\Q(\sqrt{-1}) \)

Isogeny class 54450.2-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
54450.2-i1 \( \bigl[i\) , \( -1\) , \( i\) , \( -5204\) , \( 862425\bigr] \)
54450.2-i2 \( \bigl[i\) , \( -1\) , \( i\) , \( 256\) , \( -255\bigr] \)
54450.2-i3 \( \bigl[i\) , \( -1\) , \( i\) , \( -1024\) , \( -767\bigr] \)
54450.2-i4 \( \bigl[i\) , \( -1\) , \( i\) , \( -10704\) , \( 429025\bigr] \)
54450.2-i5 \( \bigl[i\) , \( -1\) , \( i\) , \( -11824\) , \( -488927\bigr] \)
54450.2-i6 \( \bigl[i\) , \( -1\) , \( i\) , \( -171084\) , \( 27308713\bigr] \)

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