Elliptic curve isogeny class 37.1-d over number field 5.5.36497.1

• Base field: 5.5.36497.1
• Label: 5.5.36497.1-37.1-d
• Conductor: 37.1
• Rank: \( 1 \)

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 37.1-d over 5.5.36497.1

Isogeny class 37.1-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
37.1-d1	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - 2\) , \( 7 a^{4} - 48 a^{3} - 16 a^{2} + 121 a - 21\) , \( -2 a^{4} + 130 a^{3} - 11 a^{2} - 300 a + 131\bigr] \)
37.1-d2	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - 2\) , \( 2 a^{4} - 8 a^{3} - 6 a^{2} + 26 a + 14\) , \( -4 a^{3} + a^{2} + 17 a + 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph