Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5202.6-b
Conductor 5202.6
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 5202.6-b over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.6-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
5202.6-b1 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 5772 a - 561\) , \( -137153 a - 442749\bigr] \)
5202.6-b2 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -88 a - 86\) , \( -446 a + 48\bigr] \)
5202.6-b3 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -313 a - 466\) , \( 3501 a + 3002\bigr] \)
5202.6-b4 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 6672 a + 959\) , \( -150309 a - 291157\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 5 & 2 \\ 10 & 1 & 2 & 5 \\ 5 & 2 & 1 & 10 \\ 2 & 5 & 10 & 1 \end{array}\right)\)

Isogeny graph