Elliptic curve isogeny class 41.1-k over number field 6.6.1312625.1

• Base field: 6.6.1312625.1
• Label: 6.6.1312625.1-41.1-k
• Conductor: 41.1
• Rank: \( 1 \)

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-k over 6.6.1312625.1

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

Curve label	Weierstrass Coefficients
41.1-k1	\( \bigl[a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 8 a + 1\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a + 1\) , \( -7 a^{5} - 2 a^{4} + 46 a^{3} + 14 a^{2} - 62 a - 3\) , \( -62 a^{5} - 29 a^{4} + 393 a^{3} + 145 a^{2} - 534 a - 43\bigr] \)
41.1-k2	\( \bigl[a^{5} + a^{4} - 7 a^{3} - 4 a^{2} + 12 a\) , \( -a^{4} + 4 a^{2} - a\) , \( a^{5} + a^{4} - 7 a^{3} - 5 a^{2} + 12 a + 4\) , \( -180 a^{5} + 615 a^{4} + 276 a^{3} - 2589 a^{2} + 1958 a + 138\) , \( 5561 a^{5} - 14481 a^{4} - 14589 a^{3} + 60556 a^{2} - 35176 a - 3037\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph