Elliptic curve isogeny class 27.2-e over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-27.2-e
• Conductor: 27.2
• Rank: \( 1 \)

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 27.2-e over 4.4.19821.1

Isogeny class 27.2-e contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.2-e1	\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + a - 2\) , \( a^{2} - a - 4\) , \( -\frac{4}{3} a^{3} + \frac{20}{3} a^{2} - 2 a - 21\) , \( \frac{17}{3} a^{3} + \frac{8}{3} a^{2} - 66 a + 28\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph