Elliptic curve isogeny class 3.1-b over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-3.1-b
• Conductor: 3.1
• Rank: \( 1 \)

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 3.1-b over 5.5.65657.1

Isogeny class 3.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
3.1-b1	\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{2} + a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -7 a^{4} + 6 a^{3} + 24 a^{2} - 14 a - 3\) , \( -7 a^{4} + 15 a^{3} + 32 a^{2} - 29 a - 8\bigr] \)
3.1-b2	\( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 14 a^{4} - 25 a^{3} - 52 a^{2} + 68 a + 22\) , \( -22 a^{4} + 38 a^{3} + 80 a^{2} - 103 a - 29\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph