Elliptic curve isogeny class 49.2-d over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-49.2-d
• 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-d over 6.6.592661.1

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

Curve label	Weierstrass Coefficients
49.2-d1	\( \bigl[a^{5} - 4 a^{3} + a^{2} + 2 a - 3\) , \( -a^{5} + 5 a^{3} + a^{2} - 3 a - 2\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 5\) , \( 27 a^{5} - 81 a^{4} - 85 a^{3} + 376 a^{2} - 22 a - 297\) , \( 242 a^{5} - 536 a^{4} - 965 a^{3} + 2432 a^{2} + 294 a - 1763\bigr] \)
49.2-d2	\( \bigl[a^{5} - 5 a^{3} + 4 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 3 a - 4\) , \( a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + a - 4\) , \( -a^{5} + 2 a^{4} - 8 a^{2} + 5 a + 1\) , \( -4 a^{4} - a^{3} + 15 a^{2} - 4 a - 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph