Elliptic curve isogeny class 27.1-a over number field 5.5.124817.1

• Base field: 5.5.124817.1
• Label: 5.5.124817.1-27.1-a
• Conductor: 27.1
• Rank: \( 1 \)

Base field 5.5.124817.1

Generator \(a\), with minimal polynomial \( x^{5} - 7 x^{3} - 6 x^{2} + 2 x + 1 \); class number \(1\).

Elliptic curves in class 27.1-a over 5.5.124817.1

Isogeny class 27.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[3 a^{4} - 2 a^{3} - 18 a^{2} - 8 a + 4\) , \( a^{4} - 8 a^{2} - 4 a + 5\) , \( 3 a^{4} - 2 a^{3} - 19 a^{2} - 7 a + 6\) , \( 9 a^{4} - 6 a^{3} - 58 a^{2} - 19 a + 26\) , \( 13 a^{4} - 7 a^{3} - 86 a^{2} - 36 a + 38\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph