Elliptic curve isogeny class 49.1-c over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-49.1-c
• 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-c over 6.6.485125.1

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

Curve label	Weierstrass Coefficients
49.1-c1	\( \bigl[-a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 5\) , \( a^{5} - 5 a^{3} + 4 a + 1\) , \( 4 a^{5} - 7 a^{4} - 19 a^{3} + 24 a^{2} + 23 a - 7\) , \( 3 a^{5} - 3 a^{4} - 15 a^{3} + 11 a^{2} + 14 a - 5\bigr] \)
49.1-c2	\( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( a^{4} - 4 a^{2} - a + 2\) , \( 13 a^{5} - 4 a^{4} - 57 a^{3} + 5 a^{2} + 28 a - 11\) , \( 23 a^{5} - 35 a^{4} - 114 a^{3} + 128 a^{2} + 130 a - 40\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph