Elliptic curve isogeny class 20.2-a over number field 4.4.13025.1

• Base field: 4.4.13025.1
• Label: 4.4.13025.1-20.2-a
• Conductor: 20.2
• 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 20.2-a over 4.4.13025.1

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

Curve label	Weierstrass Coefficients
20.2-a1	\( \bigl[a^{2} - a - 6\) , \( -\frac{1}{2} a^{3} + 2 a^{2} + 2 a - \frac{15}{2}\) , \( a\) , \( -\frac{15}{2} a^{3} + 13 a^{2} + 30 a - \frac{81}{2}\) , \( -\frac{29}{2} a^{3} + 177 a^{2} + 65 a - \frac{1213}{2}\bigr] \)
20.2-a2	\( \bigl[a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{4}\) , \( a^{2} - 6\) , \( \frac{3}{2} a^{3} + a^{2} - 15 a - \frac{41}{2}\) , \( -\frac{9}{2} a^{3} - 4 a^{2} + 45 a + \frac{137}{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph