LMFDB - Elliptic curve isogeny class 16.1-d over number field 4.4.19225.1

Base field 4.4.19225.1

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

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

Curve label	Weierstrass Coefficients
16.1-d1	\( \bigl[-a^{3} + 4 a^{2} + 7 a - 23\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - \frac{19}{2} a + 30\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( 4 a^{3} - 13 a^{2} - 29 a + 80\) , \( \frac{3}{2} a^{3} - \frac{23}{2} a^{2} + \frac{1}{2} a + 94\bigr] \)
16.1-d2	\( \bigl[1\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{5}{2} a - 8\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( \frac{21}{2} a^{3} - \frac{73}{2} a^{2} - \frac{129}{2} a + 184\) , \( -\frac{33}{2} a^{3} + \frac{115}{2} a^{2} + \frac{203}{2} a - 290\bigr] \)

Rank: \( 1 \)

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

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