Elliptic curve isogeny class 49.2-a over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-49.2-a
• Conductor: 49.2
• Rank: \( 1 \)

Base field 6.6.592661.1

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

Elliptic curves in class 49.2-a over 6.6.592661.1

Isogeny class 49.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
49.2-a1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( a\) , \( 9 a^{5} + 10 a^{4} - 36 a^{3} - 43 a^{2} + 3 a - 6\) , \( -49 a^{5} - 33 a^{4} + 208 a^{3} + 164 a^{2} - 53 a - 19\bigr] \)
49.2-a2	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 2\) , \( a\) , \( -a^{5} + 4 a^{3} + 2 a^{2} - 2 a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph