Elliptic curve isogeny class 49.1-a over number field 6.6.1202933.1

• Base field: 6.6.1202933.1
• Label: 6.6.1202933.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

Base field 6.6.1202933.1

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

Elliptic curves in class 49.1-a over 6.6.1202933.1

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

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 2\) , \( 0\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 6 a + 3\) , \( 0\bigr] \)
49.1-a2	\( \bigl[3 a^{5} - 16 a^{3} - 7 a^{2} + 10 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 2\) , \( 0\) , \( -4 a^{5} + 24 a^{3} + 8 a^{2} - 24 a - 12\) , \( -21 a^{5} - a^{4} + 120 a^{3} + 56 a^{2} - 106 a - 55\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph