Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-100.2-a
Conductor 100.2
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 100.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 100.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
100.2-a1 \( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 4 i - 11\) , \( 11 i - 12\bigr] \)
100.2-a2 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -6 i - 11\) , \( -12 i - 12\bigr] \)
100.2-a3 \( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 54 i - 1\) , \( -119 i - 118\bigr] \)
100.2-a4 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -56 i - 1\) , \( 118 i - 118\bigr] \)
100.2-a5 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 9\) , \( 17 i\bigr] \)
100.2-a6 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 1\) , \( -i\bigr] \)
100.2-a7 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.2-a8 \( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 3 & 12 & 6 & 2 & 4 & 12 \\ 4 & 1 & 12 & 3 & 6 & 2 & 4 & 12 \\ 3 & 12 & 1 & 4 & 2 & 6 & 12 & 4 \\ 12 & 3 & 4 & 1 & 2 & 6 & 12 & 4 \\ 6 & 6 & 2 & 2 & 1 & 3 & 6 & 2 \\ 2 & 2 & 6 & 6 & 3 & 1 & 2 & 6 \\ 4 & 4 & 12 & 12 & 6 & 2 & 1 & 3 \\ 12 & 12 & 4 & 4 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph