LMFDB - Elliptic curve isogeny class 16.2-c over number field 4.4.13968.1

Base field 4.4.13968.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 4 \); class number \(1\).

Isogeny class 16.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.2-c1	\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 7 a + 4\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} - 2\bigr] \)
16.2-c2	\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -a^{3} + \frac{11}{2} a^{2} + \frac{17}{2} a - 20\) , \( \frac{11}{2} a^{3} - \frac{17}{2} a^{2} - 29 a + 42\bigr] \)

Rank: \( 0 \)

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

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