Elliptic curve isogeny class 40.1-b over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-40.1-b
• Conductor: 40.1
• 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 40.1-b over 3.3.169.1

Isogeny class 40.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
40.1-b1	\( \bigl[1\) , \( a^{2} - 3\) , \( a^{2} - a - 3\) , \( 12 a^{2} - 14 a - 42\) , \( -42 a^{2} + 54 a + 154\bigr] \)
40.1-b2	\( \bigl[1\) , \( a^{2} - 3\) , \( a^{2} - a - 3\) , \( -48 a^{2} + 56 a + 163\) , \( -133 a^{2} + 143 a + 446\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph