Elliptic curve isogeny class 27.1-b over number field 5.5.157457.1

• Base field: 5.5.157457.1
• Label: 5.5.157457.1-27.1-b
• Conductor: 27.1
• Rank: \( 1 \)

Base field 5.5.157457.1

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

Elliptic curves in class 27.1-b over 5.5.157457.1

Isogeny class 27.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 4 a - 4\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph