Elliptic curve isogeny class 49.1-b over number field 6.6.1387029.1

• Base field: 6.6.1387029.1
• Label: 6.6.1387029.1-49.1-b
• Conductor: 49.1
• Rank: \( 1 \)

Base field 6.6.1387029.1

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

Elliptic curves in class 49.1-b over 6.6.1387029.1

Isogeny class 49.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[-a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 2 a + 3\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 13 a^{2} + 5 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( 3 a^{5} - 4 a^{4} - 11 a^{3} + 11 a^{2} + 9 a - 2\) , \( 3 a^{5} - 2 a^{4} - 11 a^{3} + 6 a^{2} + 6 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph