Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-63.2-a
Conductor 63.2
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 63.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 63.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
63.2-a1 \( \bigl[1\) , \( a + 1\) , \( a\) , \( 25 a - 29\) , \( -40 a + 64\bigr] \)
63.2-a2 \( \bigl[1\) , \( a + 1\) , \( a\) , \( 10 a - 14\) , \( 20 a - 29\bigr] \)
63.2-a3 \( \bigl[1\) , \( a + 1\) , \( a\) , \( 1\) , \( a - 2\bigr] \)
63.2-a4 \( \bigl[1\) , \( a + 1\) , \( a\) , \( 155 a - 239\) , \( 1336 a - 1870\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph