Elliptic curve isogeny class 49.2-c over number field 6.6.592661.1

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

Isogeny class 49.2-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
49.2-c1	\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 6 a - 4\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( 23 a^{5} + 6 a^{4} - 108 a^{3} - 42 a^{2} + 62 a + 17\) , \( 85 a^{5} + 42 a^{4} - 373 a^{3} - 245 a^{2} + 97 a + 41\bigr] \)
49.2-c2	\( \bigl[a^{5} - a^{4} - 4 a^{3} + 5 a^{2} + 2 a - 4\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( 2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 5 a - 5\) , \( 2 a^{5} - 2 a^{4} - 7 a^{3} + 11 a^{2} + 3 a - 6\) , \( 5 a^{5} - a^{4} - 20 a^{3} + 6 a^{2} + 10 a - 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph