Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-68450.5-i
Conductor 68450.5
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 68450.5-i over \(\Q(\sqrt{-1}) \)

Isogeny class 68450.5-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
68450.5-i1 \( \bigl[i\) , \( i\) , \( i\) , \( 4 i + 6\) , \( -5 i - 6\bigr] \)
68450.5-i2 \( \bigl[i\) , \( i\) , \( i\) , \( -26 i - 34\) , \( -73 i - 30\bigr] \)
68450.5-i3 \( \bigl[i\) , \( i\) , \( i\) , \( -151 i - 209\) , \( 1177 i + 980\bigr] \)
68450.5-i4 \( \bigl[i\) , \( i\) , \( i\) , \( -381 i - 499\) , \( -5155 i - 3216\bigr] \)

Rank

Rank: \( 0 \)

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