Elliptic curve isogeny class 27.1-a over number field 3.3.761.1

• Base field: 3.3.761.1
• Label: 3.3.761.1-27.1-a
• Conductor: 27.1
• Rank: \( 1 \)

Base field 3.3.761.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 6 x - 1 \); class number \(1\).

Elliptic curves in class 27.1-a over 3.3.761.1

Isogeny class 27.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[1\) , \( a^{2} - 4\) , \( a\) , \( -a^{2} + 5 a + 3\) , \( -2 a^{2} + 6 a + 4\bigr] \)
27.1-a2	\( \bigl[1\) , \( a^{2} - 4\) , \( a\) , \( -21 a^{2} + 60 a + 13\) , \( -107 a^{2} + 301 a + 58\bigr] \)
27.1-a3	\( \bigl[1\) , \( a + 1\) , \( a^{2} - 3\) , \( -844255 a^{2} - 1742908 a - 275499\) , \( 1161532765 a^{2} + 2397908351 a + 379036571\bigr] \)
27.1-a4	\( \bigl[1\) , \( a + 1\) , \( a^{2} - 3\) , \( 15610 a^{2} + 32227 a + 5096\) , \( 61958378 a^{2} + 127909014 a + 20218533\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph