Elliptic curve isogeny class 136.1-A over number field 3.1.23.1

• Base field: 3.1.23.1
• Label: 3.1.23.1-136.1-A
• Conductor: 136.1
• 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 136.1-A over 3.1.23.1

Isogeny class 136.1-A contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
136.1-A1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \)
136.1-A2	\( \bigl[a^{2}\) , \( -1\) , \( a^{2} + 1\) , \( -a^{2} + 26 a + 21\) , \( -88 a^{2} + 13 a + 59\bigr] \)
136.1-A3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -20 a^{2} - a - 30\) , \( -38 a^{2} + 36 a - 40\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph