Elliptic curve isogeny class 27.1-b over number field 5.5.89417.1

• Base field: 5.5.89417.1
• Label: 5.5.89417.1-27.1-b
• Conductor: 27.1
• Rank: \( 0 \)

Base field 5.5.89417.1

Generator \(a\), with minimal polynomial \( x^{5} - 6 x^{3} - x^{2} + 8 x + 3 \); class number \(1\).

Elliptic curves in class 27.1-b over 5.5.89417.1

Isogeny class 27.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( -2 a^{4} + 6 a^{3} + 15 a^{2} - 16 a - 21\) , \( -4 a^{4} + 6 a^{3} + 29 a^{2} - 16 a - 42\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph