Elliptic curve isogeny class 31.1-b over number field 3.3.169.1

• Base field: 3.3.169.1
• Label: 3.3.169.1-31.1-b
• Conductor: 31.1
• 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 31.1-b over 3.3.169.1

Isogeny class 31.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
31.1-b1	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a\) , \( 668 a^{2} - 867 a - 2461\) , \( 12546 a^{2} - 16025 a - 45866\bigr] \)
31.1-b2	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a\) , \( -7 a^{2} + 8 a + 24\) , \( -4 a^{2} + 5 a + 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph