Elliptic curve isogeny class 41.1-b over number field 6.6.1312625.1

• Base field: 6.6.1312625.1
• Label: 6.6.1312625.1-41.1-b
• Conductor: 41.1
• Rank: \( 0 \)

Base field 6.6.1312625.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 7 x^{3} + 12 x^{2} - 12 x - 1 \); class number \(1\).

Elliptic curves in class 41.1-b over 6.6.1312625.1

Isogeny class 41.1-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
41.1-b1	\( \bigl[-a^{5} + 7 a^{3} + a^{2} - 10 a - 1\) , \( -a^{4} + 6 a^{2} - a - 6\) , \( a^{2} - 2\) , \( 3 a^{3} + 4 a^{2} - 8 a - 2\) , \( 2 a^{5} + 8 a^{4} - 6 a^{3} - 43 a^{2} - 3 a + 55\bigr] \)
41.1-b2	\( \bigl[a^{2} + a - 3\) , \( 2 a^{5} + a^{4} - 14 a^{3} - 5 a^{2} + 21 a + 1\) , \( a^{5} - 6 a^{3} + a^{2} + 9 a - 3\) , \( 102 a^{5} - 76 a^{4} - 608 a^{3} + 158 a^{2} + 848 a + 37\) , \( -2535 a^{5} - 1587 a^{4} + 18360 a^{3} + 6011 a^{2} - 30416 a - 2448\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph