Elliptic curve isogeny class 16.3-a over number field 4.4.13768.1

• Base field: 4.4.13768.1
• Label: 4.4.13768.1-16.3-a
• Conductor: 16.3
• Rank: \( 0 \)

Base field 4.4.13768.1

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

Elliptic curves in class 16.3-a over 4.4.13768.1

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

Curve label	Weierstrass Coefficients
16.3-a1	\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 4 a + 3\) , \( a^{2} - 2\) , \( -6 a^{3} + 5 a^{2} + 26 a - 9\) , \( 49 a^{3} - 14 a^{2} - 248 a - 86\bigr] \)
16.3-a2	\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - 4 a - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 2 a^{3} + a^{2} - 10 a - 10\) , \( a^{3} + a^{2} - 6 a - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph