Elliptic curve isogeny class 9.1-a over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-9.1-a
• Conductor: 9.1
• Rank: \( 0 \)

Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 9.1-a over 6.6.1241125.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 11 a - 5\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 3 a^{2} + 41 a + 15\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( 18 a^{5} + 6 a^{4} - 105 a^{3} - 50 a^{2} + 97 a + 43\) , \( 47 a^{5} + 62 a^{4} - 218 a^{3} - 338 a^{2} - 56 a + 22\bigr] \)
9.1-a2	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 10\) , \( -a^{5} + a^{4} + 7 a^{3} - 4 a^{2} - 11 a - 1\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( -77 a^{5} + 37 a^{4} + 522 a^{3} - 95 a^{2} - 804 a - 158\) , \( -354 a^{5} + 162 a^{4} + 2399 a^{3} - 399 a^{2} - 3697 a - 758\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph