Elliptic curve isogeny class 167.1-A over number field 3.1.23.1

• Base field: 3.1.23.1
• Label: 3.1.23.1-167.1-A
• Conductor: 167.1
• Rank: \( 0 \)

Base field 3.1.23.1

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

Elliptic curves in class 167.1-A over 3.1.23.1

Isogeny class 167.1-A contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
167.1-A1	\( \bigl[1\) , \( -a^{2} + 1\) , \( a\) , \( -a\) , \( 0\bigr] \)
167.1-A2	\( \bigl[a^{2} + a\) , \( -a^{2} - a + 1\) , \( a + 1\) , \( -86 a^{2} + 129 a - 104\) , \( -517 a^{2} + 886 a - 666\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph