Elliptic curve isogeny class 3.1-a over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-3.1-a
• Conductor: 3.1
• 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 3.1-a over 5.5.65657.1

Isogeny class 3.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
3.1-a1	\( \bigl[a^{2} - a - 2\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 12 a + 8\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( 2 a^{3} - 2 a^{2} - 8 a + 8\) , \( 4 a^{4} - 5 a^{3} - 19 a^{2} + 16 a + 11\bigr] \)
3.1-a2	\( \bigl[a^{3} - 3 a\) , \( 2 a^{4} - 3 a^{3} - 9 a^{2} + 9 a + 7\) , \( 1\) , \( 91 a^{4} + 186 a^{3} - 421 a^{2} - 905 a - 395\) , \( 2034 a^{4} + 1729 a^{3} - 9273 a^{2} - 12289 a - 3889\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph