Elliptic curve isogeny class 12.1-b over number field 3.3.564.1

• Base field: 3.3.564.1
• Label: 3.3.564.1-12.1-b
• Conductor: 12.1
• Rank: \( 1 \)

Base field 3.3.564.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 5 x + 3 \); class number \(1\).

Elliptic curves in class 12.1-b over 3.3.564.1

Isogeny class 12.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
12.1-b1	\( \bigl[a^{2} - 3\) , \( a^{2} - a - 5\) , \( a^{2} + a - 4\) , \( -208603 a^{2} + 89168 a + 1093846\) , \( -97847436 a^{2} + 41880294 a + 513193838\bigr] \)
12.1-b2	\( \bigl[a^{2} - 3\) , \( a^{2} - a - 5\) , \( a^{2} - 3\) , \( 0\) , \( -2 a^{2} - 4 a\bigr] \)
12.1-b3	\( \bigl[a^{2} - 3\) , \( a + 1\) , \( a + 1\) , \( 2520 a^{2} - 1393 a - 13872\) , \( 198755 a^{2} - 90108 a - 1052947\bigr] \)
12.1-b4	\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( 0\) , \( -1\) , \( a^{2} - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph