Elliptic curve isogeny class 37.2-b over number field 6.6.1397493.1

• Base field: 6.6.1397493.1
• Label: 6.6.1397493.1-37.2-b
• Conductor: 37.2
• Rank: \( 1 \)

Base field 6.6.1397493.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 3 x^{4} + 10 x^{3} + 3 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 37.2-b over 6.6.1397493.1

Isogeny class 37.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
37.2-b1	\( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a - 1\) , \( -a^{4} + 4 a^{3} - 8 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -5 a^{4} + 8 a^{3} + 18 a^{2} - 6 a - 3\) , \( -21 a^{5} + 22 a^{4} + 102 a^{3} - 7 a^{2} - 59 a + 14\bigr] \)
37.2-b2	\( \bigl[1\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 2 a - 4\) , \( a^{4} - 3 a^{3} - a^{2} + 6 a - 1\) , \( -a^{5} + 2 a^{4} + 9 a^{3} - 13 a^{2} - 20 a + 9\) , \( 4 a^{5} - 2 a^{4} - 20 a^{3} - 10 a^{2} + 3 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph