Elliptic curve isogeny class 25.2-a over number field 4.4.13525.1

• Base field: 4.4.13525.1
• Label: 4.4.13525.1-25.2-a
• Conductor: 25.2
• Rank: \( 0 \)

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 25.2-a over 4.4.13525.1

Isogeny class 25.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
25.2-a1	\( \bigl[\frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( -\frac{1}{5} a^{3} + \frac{2}{5} a - \frac{1}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{7}{5} a - \frac{29}{5}\) , \( a^{3} + 3 a^{2} - 6 a - 14\) , \( -\frac{74}{5} a^{3} - 30 a^{2} + \frac{423}{5} a + \frac{691}{5}\bigr] \)
25.2-a2	\( \bigl[\frac{1}{5} a^{3} - \frac{2}{5} a + \frac{1}{5}\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{7}{5} a + \frac{34}{5}\) , \( a^{2} + a - 6\) , \( \frac{17}{5} a^{3} + 2 a^{2} - \frac{194}{5} a - \frac{228}{5}\) , \( -\frac{62}{5} a^{3} - 13 a^{2} + \frac{604}{5} a + \frac{788}{5}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph