Elliptic curve isogeny class 55.1-a over number field 6.6.1541581.1

• Base field: 6.6.1541581.1
• Label: 6.6.1541581.1-55.1-a
• Conductor: 55.1
• Rank: \( 1 \)

Base field 6.6.1541581.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 2 x^{3} + 9 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 55.1-a over 6.6.1541581.1

Isogeny class 55.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
55.1-a1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 6 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 4\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 8 a^{2} + 13 a - 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 7 a - 3\) , \( 7 a^{5} - 15 a^{4} - 25 a^{3} + 43 a^{2} + 14 a - 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph