Elliptic curve isogeny class 20.4-e over number field 4.4.10025.1

• Base field: 4.4.10025.1
• Label: 4.4.10025.1-20.4-e
• Conductor: 20.4
• 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 20.4-e over 4.4.10025.1

Isogeny class 20.4-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.4-e1	\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( 5 a^{3} + 8 a^{2} - 36 a - 47\) , \( 9 a^{3} + 16 a^{2} - 66 a - 101\bigr] \)
20.4-e2	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{7}{2} a + 8\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\) , \( -4 a^{3} - 7 a^{2} + 26 a + 34\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph