Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-5202.2-e
Conductor 5202.2
Rank \( 1 \)

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 5202.2-e over \(\Q(\sqrt{-1}) \)

Isogeny class 5202.2-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
5202.2-e1 \( \bigl[i\) , \( 0\) , \( 0\) , \( -1644\) , \( 30942\bigr] \)
5202.2-e2 \( \bigl[i\) , \( 0\) , \( 0\) , \( 226\) , \( 2232\bigr] \)
5202.2-e3 \( \bigl[i\) , \( 0\) , \( 0\) , \( -114\) , \( 396\bigr] \)
5202.2-e4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \)
5202.2-e5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \)
5202.2-e6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph