Elliptic curve isogeny class 16.3-a over number field 4.4.19796.1

• Base field: 4.4.19796.1
• Label: 4.4.19796.1-16.3-a
• Conductor: 16.3
• Rank: \( 1 \)

Base field 4.4.19796.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + x + 8 \); class number \(1\).

Elliptic curves in class 16.3-a over 4.4.19796.1

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

Curve label	Weierstrass Coefficients
16.3-a1	\( \bigl[a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 5\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a + 4\) , \( -41 a^{3} - 75 a^{2} + 53 a + 98\bigr] \)
16.3-a2	\( \bigl[a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{2} - 2 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( 374 a^{3} - 1059 a^{2} - 685 a + 1639\) , \( -7492 a^{3} + 21121 a^{2} + 14015 a - 32966\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph