Elliptic curve isogeny class 20.4-a over number field 4.4.13025.1

• Base field: 4.4.13025.1
• Label: 4.4.13025.1-20.4-a
• Conductor: 20.4
• Rank: \( 0 \)

Base field 4.4.13025.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 12 x^{2} + 3 x + 29 \); class number \(1\).

Elliptic curves in class 20.4-a over 4.4.13025.1

Isogeny class 20.4-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
20.4-a1	\( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{25}{4}\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 3 a - \frac{19}{2}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( \frac{11}{4} a^{3} - \frac{7}{2} a^{2} - \frac{15}{2} a + \frac{35}{4}\) , \( -\frac{3}{2} a^{3} + 18 a^{2} + 9 a - \frac{133}{2}\bigr] \)
20.4-a2	\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 5\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - \frac{29}{4}\) , \( -\frac{45}{4} a^{3} + \frac{49}{2} a^{2} + \frac{163}{2} a - \frac{433}{4}\) , \( \frac{205}{2} a^{3} - 356 a^{2} - 608 a + \frac{4161}{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph