Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-3600.1-e
Conductor 3600.1
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 3600.1-e over \(\Q(\sqrt{2}) \)

Isogeny class 3600.1-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
3600.1-e1 \( \bigl[a\) , \( 0\) , \( a\) , \( -441\) , \( 6598\bigr] \)
3600.1-e2 \( \bigl[a\) , \( 0\) , \( a\) , \( -1\) , \( -2\bigr] \)
3600.1-e3 \( \bigl[a\) , \( 0\) , \( a\) , \( 139\) , \( 362\bigr] \)
3600.1-e4 \( \bigl[a\) , \( 0\) , \( a\) , \( -41\) , \( 38\bigr] \)
3600.1-e5 \( \bigl[a\) , \( 0\) , \( a\) , \( -21\) , \( -38\bigr] \)
3600.1-e6 \( \bigl[a\) , \( 0\) , \( a\) , \( -541\) , \( 4738\bigr] \)
3600.1-e7 \( \bigl[a\) , \( 0\) , \( a\) , \( -321\) , \( -2258\bigr] \)
3600.1-e8 \( \bigl[a\) , \( 0\) , \( a\) , \( -8641\) , \( 307678\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph