Elliptic curve isogeny class 12.1-b over number field 3.3.1076.1

• Base field: 3.3.1076.1
• Label: 3.3.1076.1-12.1-b
• Conductor: 12.1
• Rank: \( 1 \)

Base field 3.3.1076.1

Generator \(a\), with minimal polynomial \( x^{3} - 8 x - 6 \); class number \(1\).

Elliptic curves in class 12.1-b over 3.3.1076.1

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

Curve label	Weierstrass Coefficients
12.1-b1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -20508 a^{2} - 64545 a - 39093\) , \( 5222729 a^{2} + 16438176 a + 9956178\bigr] \)
12.1-b2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -1243 a^{2} - 3910 a - 2368\) , \( 84772 a^{2} + 266815 a + 161603\bigr] \)
12.1-b3	\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -2 a^{2} + 3 a + 5\) , \( 2 a^{2} - 7 a - 8\bigr] \)
12.1-b4	\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( -22 a^{2} + 58 a + 30\) , \( 152 a^{2} - 366 a - 364\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph