Elliptic curve isogeny class 37.1-a over number field 6.6.1541581.1

• Base field: 6.6.1541581.1
• Label: 6.6.1541581.1-37.1-a
• Conductor: 37.1
• Rank: \( 1 \)

Base field 6.6.1541581.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 2 x^{3} + 9 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 37.1-a over 6.6.1541581.1

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

Curve label	Weierstrass Coefficients
37.1-a1	\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + 2\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 11 a^{2} + 8 a - 2\) , \( 3 a^{5} - 3 a^{4} - 14 a^{3} + 3 a^{2} + 11 a + 3\) , \( -a^{5} + 5 a^{4} - a^{3} - 16 a^{2} + 5 a + 3\bigr] \)
37.1-a2	\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 5 a + 1\) , \( -a^{5} + a^{4} + 7 a^{3} - 4 a^{2} - 12 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( 69 a^{5} - 96 a^{4} - 379 a^{3} + 304 a^{2} + 501 a - 189\) , \( 697 a^{5} - 999 a^{4} - 3758 a^{3} + 3070 a^{2} + 4940 a - 1601\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph