Elliptic curve isogeny class 33.1-a over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-33.1-a
• Conductor: 33.1
• 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 33.1-a over 3.3.321.1

Isogeny class 33.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
33.1-a1	\( \bigl[0\) , \( -a + 1\) , \( a^{2} - 3\) , \( -14 a^{2} - 20 a + 9\) , \( 98 a^{2} + 142 a - 41\bigr] \)
33.1-a2	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -373016 a^{2} - 544785 a + 151600\) , \( 266745807 a^{2} + 389583569 a - 108411010\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph