Elliptic curve isogeny class 40.2-b over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-40.2-b
• Conductor: 40.2
• Rank: \( 0 \)

Base field 3.3.169.1

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

Elliptic curves in class 40.2-b over 3.3.169.1

Isogeny class 40.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
40.2-b1	\( \bigl[1\) , \( a^{2} - 2\) , \( 0\) , \( -3 a^{2} - 4 a\) , \( 3 a^{2} + 5 a + 1\bigr] \)
40.2-b2	\( \bigl[1\) , \( a^{2} - 2\) , \( 0\) , \( 7 a^{2} + 36 a + 5\) , \( 51 a^{2} + 145 a + 34\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph