Elliptic curve isogeny class 16.1-b over number field 3.3.756.1

• Base field: 3.3.756.1
• Label: 3.3.756.1-16.1-b
• Conductor: 16.1
• Rank: \( 1 \)

Base field 3.3.756.1

Generator \(a\), with minimal polynomial \( x^{3} - 6 x - 2 \); class number \(1\).

Elliptic curves in class 16.1-b over 3.3.756.1

Isogeny class 16.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 12 a^{2} - 6 a - 69\) , \( -60 a^{2} + 19 a + 355\bigr] \)
16.1-b2	\( \bigl[a\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 4\) , \( a + 1\) , \( -2 a - 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph