Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-64.7-g
Conductor 64.7
Rank \( 1 \)

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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 64.7-g over \(\Q(\sqrt{209}) \)

Isogeny class 64.7-g contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
64.7-g1 \( \bigl[0\) , \( -1\) , \( a\) , \( -310246949 a - 2087470581\) , \( 8088584565217 a + 54423362998209\bigr] \)
64.7-g2 \( \bigl[0\) , \( a + 1\) , \( a\) , \( -221318 a + 1710463\) , \( -9086721 a + 70225971\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph