Elliptic curve isogeny class 37.1-b over number field 5.5.24217.1

• Base field: 5.5.24217.1
• Label: 5.5.24217.1-37.1-b
• Conductor: 37.1
• Rank: \( 0 \)

Base field 5.5.24217.1

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

Elliptic curves in class 37.1-b over 5.5.24217.1

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

Curve label	Weierstrass Coefficients
37.1-b1	\( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( 0\) , \( a^{4} - 5 a^{2} + 3\) , \( 7 a^{4} + a^{3} - 36 a^{2} + 2 a\) , \( 27 a^{4} - 141 a^{2} + 20 a + 21\bigr] \)
37.1-b2	\( \bigl[3 a^{4} - a^{3} - 14 a^{2} + 3 a + 5\) , \( 0\) , \( a^{4} - 5 a^{2} + 3\) , \( -3 a^{4} + a^{3} + 14 a^{2} - 3 a - 5\) , \( -a^{4} + 5 a^{2} - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph