Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-6400.2-b
Conductor 6400.2
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 6400.2-b over \(\Q(\sqrt{-1}) \)

Isogeny class 6400.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
6400.2-b1 \( \bigl[0\) , \( i - 1\) , \( 0\) , \( 106 i - 53\) , \( 445 i + 29\bigr] \)
6400.2-b2 \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -106 i - 53\) , \( 445 i - 29\bigr] \)
6400.2-b3 \( \bigl[0\) , \( i + 1\) , \( 0\) , \( -6 i - 3\) , \( 5 i + 1\bigr] \)
6400.2-b4 \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 6 i - 3\) , \( -5 i + 1\bigr] \)
6400.2-b5 \( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -14 i - 13\) , \( -41 i - 37\bigr] \)
6400.2-b6 \( \bigl[0\) , \( i + 1\) , \( 0\) , \( 14 i - 13\) , \( 41 i - 37\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph