Elliptic curve isogeny class 40.3-b over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-40.3-b
• Conductor: 40.3
• 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 40.3-b over 3.3.169.1

Isogeny class 40.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
40.3-b1	\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( 40 a^{2} - 87 a - 54\) , \( 107 a^{2} - 248 a - 107\bigr] \)
40.3-b2	\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( -10 a^{2} + 23 a + 11\) , \( 29 a^{2} - 69 a - 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph