Elliptic curve isogeny class 9.1-a over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-9.1-a
• 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-a over 5.5.65657.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 6\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -45 a^{4} + 79 a^{3} + 158 a^{2} - 211 a - 53\) , \( -242 a^{4} + 430 a^{3} + 867 a^{2} - 1149 a - 312\bigr] \)
9.1-a2	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{4} + 5 a^{2} + 2 a - 4\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( 2 a^{4} - 2 a^{3} - 13 a^{2} + 9 a + 17\) , \( -58 a^{4} + 72 a^{3} + 271 a^{2} - 176 a - 247\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph