Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-62.2-a
Conductor 62.2
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 62.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 62.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
62.2-a1 \( \bigl[a + 1\) , \( a\) , \( a\) , \( -a - 2\) , \( 0\bigr] \)
62.2-a2 \( \bigl[a + 1\) , \( a\) , \( a\) , \( 99 a - 132\) , \( 478 a - 930\bigr] \)
62.2-a3 \( \bigl[a + 1\) , \( a\) , \( a\) , \( -106 a - 422\) , \( -1449 a - 3654\bigr] \)
62.2-a4 \( \bigl[a + 1\) , \( a\) , \( a\) , \( -21 a - 42\) , \( 52 a + 96\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph