Properties

Base field \(\Q(\sqrt{5}, \sqrt{13})\)
Label 4.4.4225.1-29.2-c
Conductor 29.2
Rank \( 0 \)

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Base field \(\Q(\sqrt{5}, \sqrt{13})\)

Generator \(a\), with minimal polynomial \( x^{4} - 9 x^{2} + 4 \); class number \(1\).

Elliptic curves in class 29.2-c over \(\Q(\sqrt{5}, \sqrt{13})\)

Isogeny class 29.2-c contains only one elliptic curve.

Curve label Weierstrass Coefficients
29.2-c1 \( \bigl[a\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{3}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( 13 a^{3} + \frac{19}{2} a^{2} - \frac{223}{2} a - 80\) , \( 54 a^{3} + \frac{73}{2} a^{2} - \frac{921}{2} a - 312\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph