Elliptic curve isogeny class 21.2-b over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-21.2-b
• 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-b over 3.3.321.1

Isogeny class 21.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
21.2-b1	\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{2} - a - 3\) , \( -230 a^{2} + 701 a - 325\) , \( 5115 a^{2} - 13492 a + 2235\bigr] \)
21.2-b2	\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{2} - a - 3\) , \( -40 a^{2} + 111 a - 25\) , \( -163 a^{2} + 450 a - 119\bigr] \)
21.2-b3	\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{2} - a - 3\) , \( -15 a^{2} + 46 a - 15\) , \( 82 a^{2} - 217 a + 42\bigr] \)
21.2-b4	\( \bigl[a + 1\) , \( a^{2} - 4\) , \( a^{2} - a - 3\) , \( a + 5\) , \( 5 a^{2} - 10 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph