Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-4.1-a
Conductor 4.1
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 4.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
4.1-a1 \( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 31\) , \( -23 a + 75\bigr] \)
4.1-a2 \( \bigl[a\) , \( 1\) , \( 0\) , \( -64 a + 209\) , \( 1147 a - 3660\bigr] \)

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Isogeny matrix

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

Isogeny graph