Elliptic curve isogeny class 3169.1-b over number field 4.4.725.1

• Base field: 4.4.725.1
• Label: 4.4.725.1-3169.1-b
• Conductor: 3169.1
• Rank: \( 1 \)

Base field 4.4.725.1

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

Elliptic curves in class 3169.1-b over 4.4.725.1

Isogeny class 3169.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
3169.1-b1	\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + 3 a\) , \( a\) , \( 5 a^{3} - 11 a^{2} + a + 1\) , \( 10 a^{3} - 23 a^{2} + 9\bigr] \)
3169.1-b2	\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + 3 a\) , \( a\) , \( -a^{2} + a + 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph