Elliptic curve isogeny class 21.2-a over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-21.2-a
• Conductor: 21.2
• 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 21.2-a over 3.3.321.1

Isogeny class 21.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
21.2-a1	\( \bigl[a\) , \( -a^{2} + 2\) , \( a + 1\) , \( 4 a^{2} - 3 a - 19\) , \( 11 a^{2} - 9 a - 48\bigr] \)
21.2-a2	\( \bigl[a\) , \( -a^{2} + 2\) , \( a + 1\) , \( -a^{2} + 7 a - 14\) , \( 9 a^{2} + 6 a - 72\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph