Elliptic curve isogeny class 16.1-a over number field 4.4.12357.1

• Base field: 4.4.12357.1
• Label: 4.4.12357.1-16.1-a
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.12357.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} + 3 x + 3 \); class number \(1\).

Elliptic curves in class 16.1-a over 4.4.12357.1

Isogeny class 16.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a^{3} - 3 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 6\) , \( a^{3} - 4 a - 1\) , \( -27 a^{3} + 38 a^{2} + 129 a - 152\) , \( -225 a^{3} + 384 a^{2} + 950 a - 1419\bigr] \)
16.1-a2	\( \bigl[a^{3} - 3 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 6\) , \( a^{3} - 4 a - 1\) , \( 3 a^{3} - 2 a^{2} - 11 a + 8\) , \( a^{3} - 2 a + 3\bigr] \)
16.1-a3	\( \bigl[a^{3} - 3 a\) , \( -a^{2} + 4\) , \( 0\) , \( a^{3} - 2 a + 5\) , \( -5 a^{3} + 9 a^{2} + 21 a - 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph