Elliptic curve isogeny class 27.2-a over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-27.2-a
• 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-a over 4.4.19821.1

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

Curve label	Weierstrass Coefficients
27.2-a1	\( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + 3 a + 1\) , \( 0\) , \( -\frac{14}{3} a^{3} - \frac{11}{3} a^{2} + 45 a + 19\) , \( -\frac{28}{3} a^{3} + \frac{20}{3} a^{2} + 54 a + 17\bigr] \)
27.2-a2	\( \bigl[a + 1\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( a^{2} - 3\) , \( -\frac{5}{3} a^{3} + \frac{1}{3} a^{2} + 10 a - 2\) , \( -\frac{7}{3} a^{3} + \frac{8}{3} a^{2} + 17 a - 22\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph