Elliptic curve isogeny class 41.3-a over number field 6.6.703493.1

• Base field: 6.6.703493.1
• Label: 6.6.703493.1-41.3-a
• Conductor: 41.3
• 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 41.3-a over 6.6.703493.1

Isogeny class 41.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41.3-a1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 1\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( -49 a^{5} + 35 a^{4} + 281 a^{3} - 160 a^{2} - 275 a + 11\) , \( 136 a^{5} - 103 a^{4} - 781 a^{3} + 472 a^{2} + 745 a - 62\bigr] \)
41.3-a2	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 1\) , \( a^{5} - 6 a^{3} + 8 a + 2\) , \( a^{5} + 5 a^{4} - 14 a^{3} - 20 a^{2} + 40 a - 9\) , \( 12 a^{5} - 24 a^{4} - 45 a^{3} + 110 a^{2} - 43 a - 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph