Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5202.5-f
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-f over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.5-f contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
5202.5-f1 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1777 a - 186\) , \( 26137 a - 30473\bigr] \)
5202.5-f2 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 8 a + 4\) , \( -a - 15\bigr] \)
5202.5-f3 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 8 a - 16\) , \( 27 a - 63\bigr] \)
5202.5-f4 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -112 a - 6\) , \( 397 a - 431\bigr] \)
5202.5-f5 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -367 a + 334\) , \( 737 a + 5859\bigr] \)
5202.5-f6 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 128 a - 346\) , \( 1449 a - 2367\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph