Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-1250.1-b
Conductor 1250.1
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 1250.1-b over \(\Q(\sqrt{2}) \)

Isogeny class 1250.1-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
1250.1-b1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \)
1250.1-b2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
1250.1-b3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \)
1250.1-b4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph