Elliptic curve isogeny class 25.1-b over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-25.1-b
• Conductor: 25.1
• Rank: \( 1 \)

Base field 5.5.65657.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 25.1-b over 5.5.65657.1

Isogeny class 25.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{4} + 5 a^{2} - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( 18 a^{4} - 34 a^{3} - 65 a^{2} + 92 a + 27\) , \( -50 a^{4} + 87 a^{3} + 183 a^{2} - 235 a - 65\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph