Properties

Base field 4.4.19821.1
Label 4.4.19821.1-48.1-f
Conductor 48.1
Rank not recorded

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Base field 4.4.19821.1

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

Elliptic curves in class 48.1-f over 4.4.19821.1

Isogeny class 48.1-f contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
48.1-f1 \( \bigl[a\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 2 a\) , \( a^{2} - 3\) , \( \frac{325}{3} a^{3} + \frac{112}{3} a^{2} - 865 a - 498\) , \( \frac{5150}{3} a^{3} + \frac{941}{3} a^{2} - 13566 a - 5705\bigr] \)
48.1-f2 \( \bigl[a\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 2 a\) , \( a^{2} - 3\) , \( \frac{5}{3} a^{3} + \frac{2}{3} a^{2} - 15 a - 8\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a - 5\bigr] \)
48.1-f3 \( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( \frac{4}{3} a^{3} + \frac{1}{3} a^{2} - 3 a + 1\) , \( \frac{13}{3} a^{3} + \frac{28}{3} a^{2} - 11 a - 5\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph