Elliptic curve isogeny class 3.1-a over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-3.1-a
• Conductor: 3.1
• 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 3.1-a over 3.3.321.1

Isogeny class 3.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
3.1-a1	\( \bigl[0\) , \( 1\) , \( a^{2} - a - 3\) , \( -767 a^{2} + 741 a - 133\) , \( 17362 a^{2} - 19422 a + 3649\bigr] \)
3.1-a2	\( \bigl[0\) , \( 1\) , \( a^{2} - a - 2\) , \( -9 a^{2} - 9 a\) , \( -62 a^{2} - 82 a + 19\bigr] \)
3.1-a3	\( \bigl[0\) , \( -a^{2} + 2\) , \( a + 1\) , \( 1197 a^{2} + 1718 a - 478\) , \( 80232 a^{2} + 117179 a - 32608\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph