Elliptic curve isogeny class 29.1-a over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-29.1-a
• Conductor: 29.1
• 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 29.1-a over 4.4.5725.1

Isogeny class 29.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.1-a1	\( \bigl[a^{2} + a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a + \frac{2}{3}\) , \( a^{2} + a - 3\) , \( -\frac{61}{3} a^{3} - 31 a^{2} + \frac{242}{3} a + \frac{251}{3}\) , \( -\frac{416}{3} a^{3} - 215 a^{2} + \frac{1678}{3} a + \frac{1786}{3}\bigr] \)
29.1-a2	\( \bigl[a\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{5}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -74 a^{3} + 254 a^{2} - 43 a - 321\) , \( \frac{2237}{3} a^{3} - 2596 a^{2} + \frac{1415}{3} a + \frac{9926}{3}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph