Properties

Base field 4.4.16225.1
Label 4.4.16225.1-16.1-a
Conductor 16.1
Rank \( 1 \)

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Base field 4.4.16225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 13 x^{2} + 6 x + 36 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.16225.1

Isogeny class 16.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[1\) , \( -\frac{1}{6} a^{3} - \frac{5}{6} a^{2} + \frac{19}{6} a + 8\) , \( \frac{1}{6} a^{3} - \frac{1}{6} a^{2} - \frac{7}{6} a\) , \( -\frac{11}{2} a^{3} + \frac{21}{2} a^{2} + \frac{95}{2} a - 65\) , \( \frac{37}{3} a^{3} - \frac{118}{3} a^{2} - \frac{289}{3} a + 299\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph