Elliptic curve isogeny class 49.1-b over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-49.1-b
• Conductor: 49.1
• Rank bounds: 0...1

Base field 4.4.19821.1

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

Elliptic curves in class 49.1-b over 4.4.19821.1

Isogeny class 49.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{2}{3} a^{3} + \frac{1}{3} a^{2} + 4 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{46}{3} a^{3} + \frac{7}{3} a^{2} - 125 a - 54\) , \( 117 a^{3} + 7 a^{2} - 929 a - 296\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph