Elliptic curve isogeny class 49.1-e over number field 6.6.1279733.1

• Base field: 6.6.1279733.1
• Label: 6.6.1279733.1-49.1-e
• Conductor: 49.1
• Rank: \( 1 \)

Base field 6.6.1279733.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 6 x^{4} + 10 x^{3} + 10 x^{2} - 11 x - 1 \); class number \(1\).

Elliptic curves in class 49.1-e over 6.6.1279733.1

Isogeny class 49.1-e contains only one elliptic curve.

Curve label	Weierstrass Coefficients
49.1-e1	\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 6 a^{2} + a - 2\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 4 a^{2} - 2 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 6 a^{2} + a - 2\) , \( a^{2} + a - 2\) , \( -a^{5} + 6 a^{4} - 4 a^{3} - 15 a^{2} + 14 a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph