Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-34000.4-a
Conductor 34000.4
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 34000.4-a over \(\Q(\sqrt{-1}) \)

Isogeny class 34000.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
34000.4-a1 \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 2134 i - 1734\) , \( -54054 i + 11448\bigr] \)
34000.4-a2 \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 134 i - 109\) , \( -854 i + 98\bigr] \)
34000.4-a3 \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 2034 i + 2066\) , \( -21644 i + 55068\bigr] \)
34000.4-a4 \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 134 i + 16\) , \( -1404 i + 1248\bigr] \)
34000.4-a5 \( \bigl[0\) , \( -i\) , \( 0\) , \( -32 i + 59\) , \( 123 i - 55\bigr] \)
34000.4-a6 \( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -1766 i - 34\) , \( -19364 i + 19028\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph