Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-1.1-a
Conductor 1.1
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 1.1-a over \(\Q(\sqrt{209}) \)

Isogeny class 1.1-a contains 2 curves linked by isogenies of degree 19.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[0\) , \( 0\) , \( 1\) , \( 12880 a - 99542\) , \( -2141323 a + 16549035\bigr] \)
1.1-a2 \( \bigl[0\) , \( 0\) , \( 1\) , \( -12880 a - 86662\) , \( 2141323 a + 14407712\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph