Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-5202.2-b
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-b over \(\Q(\sqrt{-1}) \)

Isogeny class 5202.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
5202.2-b1 \( \bigl[i\) , \( -i\) , \( 0\) , \( 1584 i + 80\) , \( 15675 i + 18965\bigr] \)
5202.2-b2 \( \bigl[1\) , \( i\) , \( 0\) , \( 99 i + 5\) , \( -240 i - 320\bigr] \)
5202.2-b3 \( \bigl[1\) , \( i\) , \( 0\) , \( 54 i - 70\) , \( -141 i - 971\bigr] \)
5202.2-b4 \( \bigl[i\) , \( -i\) , \( 0\) , \( 9 i + 5\) , \( 6 i - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph