Elliptic curve isogeny class 48.1-b over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-48.1-b
• Conductor: 48.1
• Rank: \( 0 \)

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-b over 4.4.19821.1

Isogeny class 48.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
48.1-b1	\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( -\frac{82}{3} a^{3} + \frac{113}{3} a^{2} + 211 a - 238\) , \( \frac{478}{3} a^{3} - \frac{626}{3} a^{2} - 1188 a + 1349\bigr] \)
48.1-b2	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( a^{2} - a - 4\) , \( 11 a^{3} - 7 a^{2} - 67 a - 24\) , \( -\frac{121}{3} a^{3} - \frac{160}{3} a^{2} + 444 a + 159\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph