Elliptic curve isogeny class 5.1-a over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-5.1-a
• Conductor: 5.1
• Rank: \( 0 \)

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 5.1-a over 5.5.65657.1

Isogeny class 5.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
5.1-a1	\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -3 a^{4} + 2 a^{3} + 10 a^{2} - 7 a - 3\) , \( a^{4} + 3 a^{3} - 6 a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph