Elliptic curve isogeny class 27.2-d over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-27.2-d
• Conductor: 27.2
• Rank: \( 0 \)

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-d over 4.4.19821.1

Isogeny class 27.2-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.2-d1	\( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 4 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{19}{3} a^{3} + \frac{1}{3} a^{2} - 63 a - 29\) , \( 7 a^{3} - 18 a^{2} - 128 a - 55\bigr] \)
27.2-d2	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( -a^{2} + 5\) , \( a\) , \( -a^{2} - a + 9\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph