Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-20.2-a
Conductor 20.2
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 20.2-a over \(\Q(\sqrt{29}) \)

Isogeny class 20.2-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
20.2-a1 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 142 a - 449\) , \( 1521 a - 4857\bigr] \)
20.2-a2 \( \bigl[1\) , \( a\) , \( a\) , \( -2 a - 2\) , \( -13 a - 30\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph