Elliptic curve isogeny class 41.4-b over number field 6.6.703493.1

• Base field: 6.6.703493.1
• Label: 6.6.703493.1-41.4-b
• Conductor: 41.4
• Rank: \( 0 \)

Base field 6.6.703493.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 5 x^{4} + 11 x^{3} + 2 x^{2} - 9 x + 1 \); class number \(1\).

Elliptic curves in class 41.4-b over 6.6.703493.1

Isogeny class 41.4-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41.4-b1	\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( -6 a^{5} + 5 a^{4} + 34 a^{3} - 23 a^{2} - 33 a + 4\) , \( -6 a^{5} + 3 a^{4} + 36 a^{3} - 15 a^{2} - 43 a + 5\bigr] \)
41.4-b2	\( \bigl[2 a^{5} - 2 a^{4} - 11 a^{3} + 10 a^{2} + 9 a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a^{2} - 3 a - 1\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 10 a^{2} + 17 a - 2\) , \( 19 a^{5} - 10 a^{4} - 106 a^{3} + 47 a^{2} + 92 a - 16\) , \( 55 a^{5} - 29 a^{4} - 312 a^{3} + 137 a^{2} + 286 a - 40\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph