Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-28900.6-c
Conductor 28900.6
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Rank

Rank: \( 1 \)

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

Elliptic curves in class 28900.6-c over \(\Q(\sqrt{-1}) \)

Isogeny class 28900.6-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
28900.6-c1 \( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -162 i + 124\) , \( -246 i - 1038\bigr] \)
28900.6-c2 \( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -12 i + 204\) , \( 1152 i + 170\bigr] \)
28900.6-c3 \( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -832 i - 426\) , \( -12538 i + 190\bigr] \)
28900.6-c4 \( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 818 i + 454\) , \( 1384 i + 12162\bigr] \)
28900.6-c5 \( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 73 i - 136\) , \( -750 i + 774\bigr] \)
28900.6-c6 \( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -7 i + 14\) , \( 16 i - 12\bigr] \)
28900.6-c7 \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -10 i + 20\) , \( 18 i + 9\bigr] \)
28900.6-c8 \( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -330 i + 620\) , \( -5414 i - 5123\bigr] \)