Elliptic curve isogeny class 13.1-a over number field 5.5.36497.1

• Base field: 5.5.36497.1
• Label: 5.5.36497.1-13.1-a
• Conductor: 13.1
• Rank: \( 0 \)

Base field 5.5.36497.1

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

Elliptic curves in class 13.1-a over 5.5.36497.1

Isogeny class 13.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
13.1-a1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 4\) , \( a\) , \( 53 a^{4} - 87 a^{3} - 190 a^{2} + 191 a + 122\) , \( 579 a^{4} - 931 a^{3} - 2120 a^{2} + 2049 a + 1416\bigr] \)
13.1-a2	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 2\) , \( 4 a^{4} - 6 a^{3} - 13 a^{2} + 10 a + 6\) , \( 5 a^{4} - 4 a^{3} - 19 a^{2} + 2 a + 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph