Elliptic curve isogeny class 25.1-b over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-25.1-b
• Conductor: 25.1
• Rank: \( 1 \)

Base field 4.4.5725.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 11 \); class number \(1\).

Elliptic curves in class 25.1-b over 4.4.5725.1

Isogeny class 25.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( \frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{11}{3}\) , \( a^{2} - 2 a - 5\) , \( -\frac{8}{3} a^{3} - 2 a^{2} + \frac{46}{3} a + \frac{40}{3}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph