Elliptic curve isogeny class 9.1-b over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-9.1-b
• Conductor: 9.1
• Rank: \( 1 \)

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-b over 6.6.1241125.1

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

Curve label	Weierstrass Coefficients
9.1-b1	\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 41 a - 15\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 2\) , \( 22 a^{5} + 2 a^{4} - 126 a^{3} - 50 a^{2} + 137 a + 62\) , \( -20 a^{5} - 105 a^{4} + 48 a^{3} + 445 a^{2} + 407 a + 102\bigr] \)
9.1-b2	\( \bigl[-3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 12\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 11\) , \( -8 a^{5} + 2 a^{4} + 54 a^{3} + a^{2} - 82 a - 26\) , \( 2 a^{5} - 14 a^{3} - 4 a^{2} + 22 a + 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph