Elliptic curve isogeny class 49.1-a over number field 6.6.1279733.1

• Base field: 6.6.1279733.1
• Label: 6.6.1279733.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

Base field 6.6.1279733.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 6 x^{4} + 10 x^{3} + 10 x^{2} - 11 x - 1 \); class number \(1\).

Elliptic curves in class 49.1-a over 6.6.1279733.1

Isogeny class 49.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} - a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{3} + 2 a^{2} + 3 a\) , \( 2 a^{5} - 6 a^{4} - 13 a^{3} + 32 a^{2} + 24 a - 37\bigr] \)
49.1-a2	\( \bigl[a^{4} - a^{3} - 3 a^{2} + a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 4 a + 2\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - a\) , \( 4 a^{5} + a^{4} - 28 a^{3} - 2 a^{2} + 31 a - 23\) , \( -12 a^{5} + 3 a^{4} + 62 a^{3} + a^{2} - 46 a + 31\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph