Elliptic curve isogeny class 20.2-a over number field 4.4.10025.1

• Base field: 4.4.10025.1
• Label: 4.4.10025.1-20.2-a
• Conductor: 20.2
• Rank: \( 1 \)

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 20.2-a over 4.4.10025.1

Isogeny class 20.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
20.2-a1	\( \bigl[a^{3} + 2 a^{2} - 7 a - 10\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( a + 1\) , \( -\frac{67}{2} a^{3} - \frac{105}{2} a^{2} + \frac{461}{2} a + 260\) , \( -\frac{223}{2} a^{3} - \frac{387}{2} a^{2} + \frac{1399}{2} a + 811\bigr] \)
20.2-a2	\( \bigl[a^{3} + 2 a^{2} - 6 a - 10\) , \( a^{3} + 2 a^{2} - 7 a - 12\) , \( a + 1\) , \( \frac{19}{2} a^{3} + \frac{31}{2} a^{2} - \frac{125}{2} a - 70\) , \( \frac{119}{2} a^{3} + \frac{197}{2} a^{2} - \frac{785}{2} a - 448\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph