Elliptic curve isogeny class 41.4-a over number field 6.6.703493.1

• Base field: 6.6.703493.1
• Label: 6.6.703493.1-41.4-a
• 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-a over 6.6.703493.1

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

Curve label	Weierstrass Coefficients
41.4-a1	\( \bigl[a\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 4\) , \( a^{2} + a - 2\) , \( -2 a^{5} + 13 a^{3} - 9 a^{2} - 11 a + 7\) , \( -4 a^{5} + 3 a^{4} + 10 a^{3} - 3 a^{2} - 7 a - 2\bigr] \)
41.4-a2	\( \bigl[2 a^{5} - a^{4} - 11 a^{3} + 5 a^{2} + 11 a - 1\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 2 a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 6 a^{2} + 6 a - 4\) , \( 36 a^{5} - 20 a^{4} - 199 a^{3} + 92 a^{2} + 184 a - 31\) , \( -102 a^{5} + 51 a^{4} + 576 a^{3} - 221 a^{2} - 549 a + 38\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph