Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-72.1-a
Conductor 72.1
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 72.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 72.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
72.1-a1 \( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 4\) , \( 22 i\bigr] \)
72.1-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-a3 \( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 1\) , \( -i\bigr] \)
72.1-a4 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 6\) , \( -5 i\bigr] \)
72.1-a5 \( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 16\) , \( -28 i\bigr] \)
72.1-a6 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 96\) , \( -347 i\bigr] \)

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