LMFDB - Elliptic curve isogeny class 16.1-a over number field 4.4.13025.1

Base field 4.4.13025.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 12 x^{2} + 3 x + 29 \); class number \(1\).

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + a - \frac{17}{2}\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{5}{4}\) , \( -\frac{45}{4} a^{3} - \frac{1}{2} a^{2} + \frac{207}{2} a + \frac{483}{4}\) , \( -\frac{2661}{4} a^{3} - \frac{1063}{2} a^{2} + \frac{14001}{2} a + \frac{42535}{4}\bigr] \)
16.1-a2	\( \bigl[a\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{15}{2}\) , \( a^{2} - a - 6\) , \( -18 a^{3} - 36 a^{2} + 60 a + 121\) , \( 142 a^{3} + 366 a^{2} - 457 a - 1212\bigr] \)

Rank: \( 1 \)

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

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