Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-28322.3-a
Conductor 28322.3
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 28322.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 28322.3-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
28322.3-a1 \( \bigl[i\) , \( -i\) , \( i\) , \( -1364 i + 2558\) , \( -45435 i - 41066\bigr] \)
28322.3-a2 \( \bigl[i\) , \( -i\) , \( i\) , \( -4 i + 8\) , \( 13 i + 12\bigr] \)
28322.3-a3 \( \bigl[i\) , \( -i\) , \( i\) , \( 36 i - 67\) , \( -299 i - 270\bigr] \)
28322.3-a4 \( \bigl[i\) , \( -i\) , \( i\) , \( -284 i + 533\) , \( -3627 i - 3278\bigr] \)
28322.3-a5 \( \bigl[i\) , \( -i\) , \( i\) , \( -84 i + 158\) , \( 637 i + 576\bigr] \)
28322.3-a6 \( \bigl[i\) , \( -i\) , \( i\) , \( -21844 i + 40958\) , \( -2867579 i - 2591850\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph