Elliptic curve isogeny class 25.1-d over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-25.1-d
• 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-d over 5.5.65657.1

Isogeny class 25.1-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-d1	\( \bigl[a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( a^{3} - 4 a\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 1\) , \( -32 a^{4} + 57 a^{3} + 116 a^{2} - 155 a - 42\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph