Elliptic curve isogeny class 27.3-c over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-27.3-c
• Conductor: 27.3
• Rank: \( 1 \)

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 27.3-c over 3.3.321.1

Isogeny class 27.3-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
27.3-c1	\( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( 8 a - 22\) , \( 18 a^{2} + 34 a - 194\bigr] \)
27.3-c2	\( \bigl[a^{2} - a - 2\) , \( -1\) , \( a\) , \( -2 a + 3\) , \( -a^{2} - a + 7\bigr] \)
27.3-c3	\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( 1\) , \( -64 a^{2} + 212 a - 129\) , \( 840 a^{2} - 2353 a + 707\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph