Elliptic curve isogeny class 27.1-e over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-27.1-e
• Conductor: 27.1
• 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 27.1-e over 5.5.65657.1

Isogeny class 27.1-e contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-e1	\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 4\) , \( 2 a^{4} - 8 a^{3} + 5 a^{2} + 6 a + 1\) , \( -2 a^{4} + 5 a^{3} + a^{2} - 5 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph