Elliptic curve isogeny class 25.1-a over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-25.1-a
• Conductor: 25.1
• Rank: \( 0 \)

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 25.1-a over 4.4.4525.1

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

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a\) , \( \frac{1}{3} a^{3} - \frac{4}{3} a^{2} - \frac{4}{3} a + 3\) , \( a + 1\) , \( -3 a^{3} - 2 a^{2} + 18 a + 20\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + 2\bigr] \)
25.1-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( \frac{22}{3} a^{3} - \frac{40}{3} a^{2} - \frac{100}{3} a + 52\) , \( \frac{26}{3} a^{3} - \frac{44}{3} a^{2} - \frac{122}{3} a + 55\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph