Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-50.4-b
Conductor 50.4
Rank \( 1 \)

Related objects

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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 50.4-b over \(\Q(\sqrt{209}) \)

Isogeny class 50.4-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
50.4-b1 \( \bigl[a\) , \( a\) , \( 1\) , \( -4988005 a - 33561363\) , \( 16267292978 a + 109453116751\bigr] \)
50.4-b2 \( \bigl[a\) , \( -1\) , \( 1\) , \( 4 a + 66\) , \( 16 a + 149\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph