Elliptic curve isogeny class 41.3-f over number field 6.6.980125.1

• Base field: 6.6.980125.1
• Label: 6.6.980125.1-41.3-f
• Conductor: 41.3
• Rank: \( 0 \)

Base field 6.6.980125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 7 x^{2} - 5 x - 1 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 41.3-f over 6.6.980125.1

Isogeny class 41.3-f contains only one elliptic curve.

Curve label	Weierstrass Coefficients
41.3-f1	\( \bigl[a^{5} + a^{4} - 5 a^{3} - 3 a^{2} + 5 a\) , \( -2 a^{4} - a^{3} + 9 a^{2} + 3 a - 3\) , \( a^{5} + 2 a^{4} - 5 a^{3} - 8 a^{2} + 6 a + 3\) , \( -5 a^{5} - a^{4} + 25 a^{3} - 2 a^{2} - 18 a + 8\) , \( -21 a^{5} + 18 a^{4} + 118 a^{3} - 114 a^{2} - 112 a + 100\bigr] \)