Elliptic curve isogeny class 20.1-a over number field 4.4.18625.1

• Base field: 4.4.18625.1
• Label: 4.4.18625.1-20.1-a
• Conductor: 20.1
• Rank: \( 1 \)

Base field 4.4.18625.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 14 x^{2} + 9 x + 41 \); class number \(1\).

Elliptic curves in class 20.1-a over 4.4.18625.1

Isogeny class 20.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{7}{6} a^{3} - a^{2} + \frac{31}{3} a + \frac{71}{6}\) , \( \frac{413}{6} a^{3} + 103 a^{2} - \frac{2147}{3} a - \frac{6973}{6}\bigr] \)
20.1-a2	\( \bigl[1\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{7}{6}\) , \( -\frac{25}{3} a^{3} - 21 a^{2} + \frac{170}{3} a + \frac{347}{3}\) , \( \frac{269}{6} a^{3} + 82 a^{2} - \frac{839}{3} a - \frac{2905}{6}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph