Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-16.4-a
Conductor 16.4
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 16.4-a over \(\Q(\sqrt{209}) \)

Isogeny class 16.4-a contains 2 curves linked by isogenies of degree 11.

Curve label Weierstrass Coefficients
16.4-a1 \( \bigl[0\) , \( a - 1\) , \( a\) , \( -317 a - 2113\) , \( 7753 a + 52137\bigr] \)
16.4-a2 \( \bigl[0\) , \( -a\) , \( a\) , \( 931337 a - 7197740\) , \( 1351685914 a - 10446391276\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph