Elliptic curve isogeny class 16.1-a over number field 4.4.10025.1

• Base field: 4.4.10025.1
• Label: 4.4.10025.1-16.1-a
• Conductor: 16.1
• 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 16.1-a over 4.4.10025.1

Isogeny class 16.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 8\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 9\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( \frac{9}{2} a^{3} + \frac{17}{2} a^{2} - \frac{59}{2} a - 42\) , \( \frac{5}{2} a^{3} + \frac{9}{2} a^{2} - \frac{33}{2} a - 22\bigr] \)
16.1-a2	\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( a^{2} - a - 6\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( -\frac{409}{2} a^{3} + \frac{863}{2} a^{2} + \frac{3649}{2} a - 4045\) , \( -5735 a^{3} + 11714 a^{2} + 50945 a - 110458\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph