Properties

Base field 4.4.19225.1
Label 4.4.19225.1-29.1-a
Conductor 29.1
Rank \( 1 \)

Related objects

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Base field 4.4.19225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 15 x^{2} + 2 x + 44 \); class number \(1\).

Elliptic curves in class 29.1-a over 4.4.19225.1

Isogeny class 29.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
29.1-a1 \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 8\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{21}{2} a + 32\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -59 a^{3} + 194 a^{2} + 433 a - 1112\) , \( 406 a^{3} - 1360 a^{2} - 2899 a + 7616\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph