Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-1225.1-e
Conductor 1225.1
Rank \( 1 \)

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 1225.1-e over \(\Q(\sqrt{2}) \)

Isogeny class 1225.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1225.1-e1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 78 a - 172\) , \( 422 a - 1023\bigr] \)
1225.1-e2 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -2 a - 2\) , \( -2 a - 3\bigr] \)
1225.1-e3 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -22 a - 47\) , \( -108 a - 168\bigr] \)
1225.1-e4 \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 213 a - 337\) , \( 1798 a - 2604\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph