Elliptic curve isogeny class 89.1-A over number field 3.1.23.1

• Base field: 3.1.23.1
• Label: 3.1.23.1-89.1-A
• Conductor: 89.1
• 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 89.1-A over 3.1.23.1

Isogeny class 89.1-A contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
89.1-A1	\( \bigl[a + 1\) , \( -a^{2} - a - 1\) , \( a^{2} + a\) , \( -a^{2}\) , \( -a^{2} + 1\bigr] \)
89.1-A2	\( \bigl[a + 1\) , \( -a^{2} - a - 1\) , \( a^{2} + a\) , \( -6 a^{2} + 5 a - 5\) , \( 5 a^{2} - 11 a + 9\bigr] \)
89.1-A3	\( \bigl[a^{2} + a + 1\) , \( -a^{2} - 1\) , \( a^{2} + 1\) , \( -133 a^{2} + 216 a - 155\) , \( -870 a^{2} + 1533 a - 1172\bigr] \)
89.1-A4	\( \bigl[a + 1\) , \( -a^{2} - a - 1\) , \( a^{2} + a\) , \( -31 a^{2} + 80 a - 50\) , \( -115 a^{2} + 276 a - 245\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 10 & 5 \\ 2 & 1 & 5 & 10 \\ 10 & 5 & 1 & 2 \\ 5 & 10 & 2 & 1 \end{array}\right)\)

Isogeny graph