Elliptic curve isogeny class 25.1-a over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-25.1-a
• 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-a over 4.4.5725.1

Isogeny class 25.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[\frac{1}{3} a^{3} + a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( a^{2} + a - 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a + \frac{1}{3}\) , \( \frac{10}{3} a^{3} + 3 a^{2} - \frac{41}{3} a - \frac{17}{3}\) , \( 4 a^{3} + 8 a^{2} - 16 a - 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph