Elliptic curve isogeny class 20.1-d over number field 4.4.18625.1

• Base field: 4.4.18625.1
• Label: 4.4.18625.1-20.1-d
• 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-d over 4.4.18625.1

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

Curve label	Weierstrass Coefficients
20.1-d1	\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{1}{3} a + \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( \frac{3}{2} a^{3} - a^{2} - 10 a + \frac{19}{2}\) , \( \frac{5}{6} a^{3} + 3 a^{2} - \frac{23}{3} a - \frac{73}{6}\bigr] \)
20.1-d2	\( \bigl[a\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{4}{3} a - \frac{43}{6}\) , \( 1\) , \( \frac{5}{6} a^{3} - \frac{47}{3} a - \frac{73}{6}\) , \( -\frac{21}{2} a^{3} - 19 a^{2} + 84 a + \frac{275}{2}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph