Elliptic curve isogeny class 29.2-a over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-29.2-a
• Conductor: 29.2
• Rank: \( 0 \)

Base field 4.4.5725.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 11 \); class number \(1\).

Elliptic curves in class 29.2-a over 4.4.5725.1

Isogeny class 29.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.2-a1	\( \bigl[a^{2} + a - 4\) , \( \frac{1}{3} a^{3} - a^{2} - \frac{5}{3} a + \frac{10}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{44}{3} a^{3} + 28 a^{2} + \frac{268}{3} a - \frac{518}{3}\) , \( -\frac{362}{3} a^{3} + 232 a^{2} + \frac{2242}{3} a - \frac{4247}{3}\bigr] \)
29.2-a2	\( \bigl[a^{2} - 3\) , \( -\frac{1}{3} a^{3} + a^{2} + \frac{8}{3} a - \frac{10}{3}\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -46 a^{3} - 32 a^{2} + 294 a + 225\) , \( \frac{361}{3} a^{3} + 115 a^{2} - \frac{2312}{3} a - \frac{2348}{3}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph