Elliptic curve isogeny class 9.1-b over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-9.1-b
• Conductor: 9.1
• Rank: \( 0 \)

Base field 5.5.65657.1

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

Elliptic curves in class 9.1-b over 5.5.65657.1

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

Curve label	Weierstrass Coefficients
9.1-b1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 2\) , \( a^{3} - 3 a\) , \( -a^{3} - a^{2} + 2 a + 4\) , \( 2 a^{4} - 3 a^{3} - 10 a^{2} + 7 a + 8\bigr] \)
9.1-b2	\( \bigl[a^{3} - 4 a - 1\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - 2\) , \( 17 a^{4} + 247 a^{3} - 506 a^{2} - 251 a - 16\) , \( 3325 a^{4} - 6557 a^{3} - 5396 a^{2} + 5378 a + 1457\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph