Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-225.2-a
Conductor 225.2
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 225.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 225.2-a contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
225.2-a1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -105 i + 395\) , \( -2982 i - 1054\bigr] \)
225.2-a2 \( \bigl[i\) , \( -1\) , \( i\) , \( 105 i + 396\) , \( -2982 i + 1054\bigr] \)
225.2-a3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
225.2-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
225.2-a5 \( \bigl[i\) , \( -1\) , \( i\) , \( 36\) , \( 28\bigr] \)
225.2-a6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
225.2-a7 \( \bigl[i\) , \( -1\) , \( i\) , \( -4\) , \( -2\bigr] \)
225.2-a8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
225.2-a9 \( \bigl[i\) , \( -1\) , \( i\) , \( -79\) , \( -242\bigr] \)
225.2-a10 \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 16 & 16 & 2 & 4 & 8 & 8 & 16 & 16 \\ 4 & 1 & 16 & 16 & 2 & 4 & 8 & 8 & 16 & 16 \\ 16 & 16 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 2 & 2 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 8 & 8 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 16 & 16 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph