Elliptic curve isogeny class 37.1-b over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-37.1-b
• Conductor: 37.1
• Rank: \( 0 \)

Base field 5.5.38569.1

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

Elliptic curves in class 37.1-b over 5.5.38569.1

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

Curve label	Weierstrass Coefficients
37.1-b1	\( \bigl[0\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( a^{3} - 3 a + 1\) , \( -5 a^{4} - a^{3} + 24 a^{2} + 5 a - 15\) , \( a^{4} - 5 a^{2} - a + 3\bigr] \)
37.1-b2	\( \bigl[0\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 4\) , \( a^{3} - 3 a + 1\) , \( -155 a^{4} - 41 a^{3} + 764 a^{2} + 205 a - 565\) , \( -1406 a^{4} - 388 a^{3} + 6922 a^{2} + 1910 a - 5100\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph