Elliptic curve isogeny class 5.2-a over number field 4.4.13525.1

• Base field: 4.4.13525.1
• Label: 4.4.13525.1-5.2-a
• Conductor: 5.2
• Rank: \( 1 \)

Base field 4.4.13525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 12 x^{2} + 8 x + 29 \); class number \(1\).

Elliptic curves in class 5.2-a over 4.4.13525.1

Isogeny class 5.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
5.2-a1	\( \bigl[1\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{24}{5}\) , \( a^{2} + a - 6\) , \( \frac{12}{5} a^{3} + 4 a^{2} - \frac{74}{5} a - \frac{88}{5}\) , \( \frac{16}{5} a^{3} + 8 a^{2} - \frac{87}{5} a - \frac{199}{5}\bigr] \)
5.2-a2	\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{34}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{18}{5} a^{3} - 8 a^{2} + \frac{116}{5} a + \frac{212}{5}\) , \( -\frac{41}{5} a^{3} - 16 a^{2} + \frac{237}{5} a + \frac{384}{5}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph