Elliptic curve isogeny class 49.1-f over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-49.1-f
• Conductor: 49.1
• Rank: \( 1 \)

Base field 6.6.485125.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1 \); class number \(1\).

Elliptic curves in class 49.1-f over 6.6.485125.1

Isogeny class 49.1-f contains only one elliptic curve.

Curve label	Weierstrass Coefficients
49.1-f1	\( \bigl[a + 1\) , \( -3 a^{5} + 4 a^{4} + 13 a^{3} - 14 a^{2} - 9 a + 5\) , \( 2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( -4 a^{5} + 2 a^{4} + 20 a^{3} - 6 a^{2} - 21 a + 3\) , \( -3 a^{5} + 3 a^{4} + 14 a^{3} - 10 a^{2} - 13 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph