Elliptic curve isogeny class 25.3-b over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-25.3-b
• Conductor: 25.3
• 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 25.3-b over 4.4.4525.1

Isogeny class 25.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
25.3-b1	\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + \frac{1}{3} a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( 2 a^{2} - 4 a - 3\) , \( -\frac{2}{3} a^{3} + \frac{2}{3} a^{2} + \frac{8}{3} a - 1\bigr] \)
25.3-b2	\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( -a^{2} + 2 a + 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{13}{3} a - 3\) , \( \frac{10}{3} a^{3} + \frac{2}{3} a^{2} - \frac{64}{3} a - 21\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph