Elliptic curve isogeny class 25.2-c over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-25.2-c
• Conductor: 25.2
• Rank: \( 1 \)

Base field 4.4.4525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 3 x + 9 \); class number \(1\).

Elliptic curves in class 25.2-c over 4.4.4525.1

Isogeny class 25.2-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
25.2-c1	\( \bigl[0\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{7}{3} a + 9\) , \( -a^{3} + 2 a^{2} + 3 a - 9\bigr] \)
25.2-c2	\( \bigl[0\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 4\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{7}{3} a\) , \( \frac{2}{3} a^{3} + \frac{1}{3} a^{2} - \frac{14}{3} a - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph