Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5202.5-i
Conductor 5202.5
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 5202.5-i over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.5-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
5202.5-i1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \)
5202.5-i2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 4305 a - 924\) , \( -137739 a - 127314\bigr] \)
5202.5-i3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -4305 a - 924\) , \( 137739 a - 127314\bigr] \)
5202.5-i4 \( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \)
5202.5-i5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \)
5202.5-i6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \)
5202.5-i7 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \)
5202.5-i8 \( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 8 & 4 & 8 & 2 & 4 \\ 2 & 1 & 4 & 16 & 8 & 16 & 4 & 8 \\ 2 & 4 & 1 & 16 & 8 & 16 & 4 & 8 \\ 8 & 16 & 16 & 1 & 2 & 4 & 4 & 8 \\ 4 & 8 & 8 & 2 & 1 & 2 & 2 & 4 \\ 8 & 16 & 16 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 4 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 8 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph