LMFDB - Elliptic curve isogeny class 48.1-a over number field 4.4.19821.1

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Isogeny class 48.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
48.1-a1	\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 5 a + 2\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( -\frac{8}{3} a^{3} + \frac{10}{3} a^{2} + 21 a - 21\) , \( -\frac{38}{3} a^{3} + \frac{52}{3} a^{2} + 96 a - 111\bigr] \)
48.1-a2	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 4\) , \( 0\) , \( \frac{119}{3} a^{3} - \frac{142}{3} a^{2} - 150 a - 126\) , \( 2041 a^{3} - 6773 a^{2} + 2003 a + 1146\bigr] \)

Rank: \( 0 \)

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

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