Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-22050.2-e
Conductor 22050.2
Rank \( 0 \)

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 22050.2-e over \(\Q(\sqrt{-1}) \)

Isogeny class 22050.2-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
22050.2-e1 \( \bigl[i\) , \( -1\) , \( i\) , \( -979\) , \( 15325\bigr] \)
22050.2-e2 \( \bigl[i\) , \( -1\) , \( i\) , \( 11\) , \( 13\bigr] \)
22050.2-e3 \( \bigl[i\) , \( -1\) , \( i\) , \( -69\) , \( 205\bigr] \)
22050.2-e4 \( \bigl[i\) , \( -1\) , \( i\) , \( -369\) , \( -2435\bigr] \)
22050.2-e5 \( \bigl[i\) , \( -1\) , \( i\) , \( -1049\) , \( 13533\bigr] \)
22050.2-e6 \( \bigl[i\) , \( -1\) , \( i\) , \( -16799\) , \( 845133\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph