Elliptic curve isogeny class 16.1-e over number field 4.4.13025.1

• Base field: 4.4.13025.1
• Label: 4.4.13025.1-16.1-e
• Conductor: 16.1
• Rank: \( 1 \)

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 16.1-e over 4.4.13025.1

Isogeny class 16.1-e contains only one elliptic curve.

Curve label	Weierstrass Coefficients
16.1-e1	\( \bigl[-\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( -\frac{1}{2} a^{3} + 3 a^{2} + 3 a - \frac{21}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{3}{4}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph