Elliptic curve isogeny class 107.1-A over number field 3.1.23.1

• Base field: 3.1.23.1
• Label: 3.1.23.1-107.1-A
• Conductor: 107.1
• 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 107.1-A over 3.1.23.1

Isogeny class 107.1-A contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
107.1-A1	\( \bigl[0\) , \( a^{2} + a - 1\) , \( a^{2} + 1\) , \( a^{2} - a - 1\) , \( -a^{2}\bigr] \)
107.1-A2	\( \bigl[0\) , \( a^{2} - a + 1\) , \( a^{2} + a\) , \( -30 a^{2} - 11 a + 11\) , \( -101 a^{2} + 29 a + 80\bigr] \)
107.1-A3	\( \bigl[0\) , \( -a^{2} - a\) , \( 1\) , \( -59 a^{2} + 100 a - 71\) , \( -274 a^{2} + 484 a - 422\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph