Elliptic curve isogeny class 49.1-b over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-49.1-b
• Conductor: 49.1
• Rank: \( 0 \)

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-b over 6.6.485125.1

Isogeny class 49.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 2 a + 3\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a - 1\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( a^{5} - 4 a^{4} - 8 a^{3} + 14 a^{2} + 9 a - 10\) , \( 6 a^{5} - 4 a^{4} - 24 a^{3} + 17 a^{2} + 13 a - 14\bigr] \)
49.1-b2	\( \bigl[a^{4} - 3 a^{2} - a + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + a + 4\) , \( a^{5} - 5 a^{3} + 4 a\) , \( a^{5} - 5 a^{4} - 6 a^{3} + 16 a^{2} + 3 a - 5\) , \( -17 a^{5} - 12 a^{4} + 59 a^{3} + 37 a^{2} - 26 a - 15\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph