Elliptic curve isogeny class 16.3-a over number field 4.4.13068.1

• Base field: 4.4.13068.1
• Label: 4.4.13068.1-16.3-a
• Conductor: 16.3
• Rank: \( 0 \)

Base field 4.4.13068.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 16.3-a over 4.4.13068.1

Isogeny class 16.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
16.3-a1	\( \bigl[0\) , \( -a^{3} + a^{2} + 7 a + 2\) , \( a^{2} - a - 3\) , \( -a^{3} + a^{2} + 7 a + 4\) , \( 2 a^{3} - 2 a^{2} - 14 a - 8\bigr] \)
16.3-a2	\( \bigl[0\) , \( a^{2} - 2 a - 2\) , \( a^{2} - a - 3\) , \( -a^{3} + 2 a^{2} + 3 a + 1\) , \( 3 a^{3} + 6 a^{2} - 2 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph