Elliptic curve isogeny class 27.1-b over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-27.1-b
• Conductor: 27.1
• Rank: \( 0 \)

Base field 3.3.321.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 1 \); class number \(1\).

Elliptic curves in class 27.1-b over 3.3.321.1

Isogeny class 27.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[0\) , \( -a + 1\) , \( a^{2} - a - 2\) , \( 76 a^{2} + 83 a - 24\) , \( -1175 a^{2} - 1748 a + 484\bigr] \)
27.1-b2	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 122 a^{2} - 92 a - 516\) , \( 1124 a^{2} - 848 a - 4709\bigr] \)
27.1-b3	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -409 a^{2} + 1027 a - 222\) , \( 8470 a^{2} - 23221 a + 5068\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph