Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-648.1-a
Conductor 648.1
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 648.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 648.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
648.1-a1 \( \bigl[a\) , \( 1\) , \( a\) , \( 4590 a - 7345\) , \( -215622 a + 314563\bigr] \)
648.1-a2 \( \bigl[a\) , \( 1\) , \( a\) , \( 35\) , \( 607\bigr] \)
648.1-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \)
648.1-a4 \( \bigl[a\) , \( 1\) , \( a\) , \( -10\) , \( -14\bigr] \)
648.1-a5 \( \bigl[a\) , \( 1\) , \( a\) , \( -55\) , \( 121\bigr] \)
648.1-a6 \( \bigl[a\) , \( 1\) , \( a\) , \( -145\) , \( -743\bigr] \)
648.1-a7 \( \bigl[a\) , \( 1\) , \( a\) , \( -865\) , \( 9355\bigr] \)
648.1-a8 \( \bigl[a\) , \( 1\) , \( a\) , \( -4590 a - 7345\) , \( 215622 a + 314563\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph