Elliptic curve isogeny class 16.1-b over number field 4.4.17725.1

• Base field: 4.4.17725.1
• Label: 4.4.17725.1-16.1-b
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.17725.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 12 x^{2} + 13 x + 41 \); class number \(1\).

Elliptic curves in class 16.1-b over 4.4.17725.1

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

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[a^{3} - 7 a - 7\) , \( a^{3} - 7 a - 7\) , \( 0\) , \( 8 a^{3} - 2 a^{2} - 47 a - 38\) , \( 3 a^{3} + 42 a^{2} - 64 a - 234\bigr] \)
16.1-b2	\( \bigl[1\) , \( -a^{2} + a + 8\) , \( a + 1\) , \( -3 a^{2} + a + 19\) , \( a^{3} - a^{2} - 7 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph