Elliptic curve isogeny class 41.1-a over number field 6.6.1683101.1

• Base field: 6.6.1683101.1
• Label: 6.6.1683101.1-41.1-a
• Conductor: 41.1
• Rank: \( 2 \)

Base field 6.6.1683101.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 4 x^{4} + 13 x^{3} + 7 x^{2} - 14 x - 7 \); class number \(1\).

Elliptic curves in class 41.1-a over 6.6.1683101.1

Isogeny class 41.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
41.1-a1	\( \bigl[a^{3} - 3 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 9 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 6 a^{5} - 7 a^{4} - 35 a^{3} + 14 a^{2} + 61 a + 23\) , \( 8 a^{5} - 8 a^{4} - 47 a^{3} + 14 a^{2} + 81 a + 33\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph