Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-16.1-a
Conductor 16.1
Rank not recorded

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Base field \(\Q(\sqrt{29}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 7 \); class number \(1\).

Elliptic curves in class 16.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 1\) , \( -3 a - 7\bigr] \)
16.1-a2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 3\) , \( 3 a - 10\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph