Elliptic curve isogeny class 20.1-g over number field 4.4.10025.1

• Base field: 4.4.10025.1
• Label: 4.4.10025.1-20.1-g
• Conductor: 20.1
• Rank: \( 0 \)

Base field 4.4.10025.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 10 x + 20 \); class number \(1\).

Elliptic curves in class 20.1-g over 4.4.10025.1

Isogeny class 20.1-g contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
20.1-g1	\( \bigl[a^{3} + 2 a^{2} - 6 a - 11\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{9}{2} a - 3\) , \( 1\) , \( 3 a^{3} - a^{2} - 24 a + 27\) , \( \frac{7}{2} a^{3} + \frac{5}{2} a^{2} - \frac{55}{2} a + 1\bigr] \)
20.1-g2	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( \frac{3}{2} a^{3} - \frac{81}{2} a^{2} + \frac{97}{2} a + 97\) , \( 72 a^{3} - 267 a^{2} + 51 a + 420\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph