Elliptic curve isogeny class 27.2-c over number field 4.4.19821.1

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

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

Curve label	Weierstrass Coefficients
27.2-c1	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( a\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} - a + 2\) , \( a^{3} - 3 a^{2} + 2 a\bigr] \)
27.2-c2	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 2\) , \( a\) , \( 18 a^{3} - 65 a^{2} + 34 a + 12\) , \( \frac{701}{3} a^{3} - \frac{2560}{3} a^{2} + 416 a + 253\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph