Elliptic Curve Isogeny Class 49.1-a over Number Field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-49.1-a
• Conductor: 49.1
• Rank: not recorded

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-a over 6.6.485125.1

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

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 3 a + 3\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 5 a - 1\) , \( a^{4} - a^{3} - 3 a^{2} + 3 a + 2\) , \( 4 a^{5} - 8 a^{4} - 16 a^{3} + 32 a^{2} + 10 a - 24\) , \( -21 a^{5} + 37 a^{4} + 92 a^{3} - 148 a^{2} - 74 a + 90\bigr] \)
49.1-a2	\( \bigl[a^{2} + a - 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 10 a^{2} + 6 a - 3\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 3 a + 4\) , \( -6 a^{5} + 2 a^{4} + 42 a^{3} + 5 a^{2} - 71 a - 40\) , \( 11 a^{5} + 11 a^{4} - 89 a^{3} - 91 a^{2} + 157 a + 153\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph