Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-2.1-c
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-c over \(\Q(\sqrt{209}) \)

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

Curve label Weierstrass Coefficients
2.1-c1 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 1502 a - 11391\) , \( 84221 a - 650261\bigr] \)
2.1-c2 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 8 a + 57\) , \( 19 a + 137\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph