Elliptic curve isogeny class 16.1-a over number field 4.4.19225.1

• Base field: 4.4.19225.1
• Label: 4.4.19225.1-16.1-a
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.19225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 15 x^{2} + 2 x + 44 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.19225.1

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

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{3}{2} a + 14\) , \( -a^{3} + 4 a^{2} + 7 a - 23\) , \( -\frac{11}{2} a^{3} + \frac{33}{2} a^{2} + \frac{77}{2} a - 72\) , \( -\frac{417}{2} a^{3} + \frac{1461}{2} a^{2} + \frac{2581}{2} a - 3635\bigr] \)
16.1-a2	\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( -\frac{3}{2} a^{3} + \frac{11}{2} a^{2} + \frac{17}{2} a - 32\) , \( a\) , \( -a^{3} + 4 a^{2} + 7 a - 15\) , \( -\frac{5}{2} a^{3} + \frac{1}{2} a^{2} + \frac{31}{2} a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph