Elliptic curve isogeny class 37.1-b over number field 5.5.36497.1

• Base field: 5.5.36497.1
• Label: 5.5.36497.1-37.1-b
• Conductor: 37.1
• 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 37.1-b over 5.5.36497.1

Isogeny class 37.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
37.1-b1	\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 4\) , \( a^{2} - a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - a^{2} + a - 2\) , \( -4 a^{4} + 5 a^{3} + 15 a^{2} - 12 a - 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph