Elliptic curve isogeny class 25.1-a over number field 4.4.13525.1

• Base field: 4.4.13525.1
• Label: 4.4.13525.1-25.1-a
• Conductor: 25.1
• 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 25.1-a over 4.4.13525.1

Isogeny class 25.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[a^{2} - 5\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{12}{5} a - \frac{24}{5}\) , \( a^{2} - 5\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( -3 a^{3} - 3 a^{2} + 15 a + 17\bigr] \)
25.1-a2	\( \bigl[a + 1\) , \( -\frac{1}{5} a^{3} - a^{2} + \frac{2}{5} a + \frac{29}{5}\) , \( \frac{1}{5} a^{3} + a^{2} - \frac{2}{5} a - \frac{29}{5}\) , \( -\frac{144}{5} a^{3} + 67 a^{2} + \frac{1218}{5} a - \frac{2799}{5}\) , \( \frac{969}{5} a^{3} - 476 a^{2} - \frac{8253}{5} a + \frac{19714}{5}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph