Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-2.1-b
Conductor 2.1
Rank not recorded

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Base field \(\Q(\sqrt{209}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 52 \); class number \(1\).

Elliptic curves in class 2.1-b over \(\Q(\sqrt{209}) \)

Isogeny class 2.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
2.1-b1 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -166349 a - 1119240\) , \( -101485499 a - 682836650\bigr] \)
2.1-b2 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -6449241 a + 49842606\) , \( -1496864675 a + 11568393744\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph