Elliptic curve isogeny class 259.1-A over number field 3.1.23.1

• Base field: 3.1.23.1
• Label: 3.1.23.1-259.1-A
• Conductor: 259.1
• 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 259.1-A over 3.1.23.1

Isogeny class 259.1-A contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
259.1-A1	\( \bigl[0\) , \( a^{2}\) , \( 1\) , \( -a\) , \( 0\bigr] \)
259.1-A2	\( \bigl[0\) , \( a^{2}\) , \( 1\) , \( 9 a\) , \( 8 a^{2} - 15\bigr] \)
259.1-A3	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -1768 a^{2} + 3086 a - 2357\) , \( -52408 a^{2} + 92024 a - 69423\bigr] \)
259.1-A4	\( \bigl[0\) , \( a^{2} + a - 1\) , \( a + 1\) , \( -1159242728 a^{2} + 2034329174 a - 1535669655\) , \( -27257216724773 a^{2} + 47833080874361 a - 36108124459830\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 27 & 9 \\ 3 & 1 & 9 & 3 \\ 27 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph