Elliptic curve isogeny class 16.1-c over number field 4.4.17725.1

• Base field: 4.4.17725.1
• Label: 4.4.17725.1-16.1-c
• Conductor: 16.1
• Rank bounds: 0...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-c over 4.4.17725.1

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

Curve label	Weierstrass Coefficients
16.1-c1	\( \bigl[a^{3} - 7 a - 7\) , \( -a^{3} + 7 a + 8\) , \( a\) , \( -155 a^{3} - 181 a^{2} + 1187 a + 1810\) , \( -2555 a^{3} - 3316 a^{2} + 19512 a + 31312\bigr] \)
16.1-c2	\( \bigl[a^{3} - a^{2} - 7 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a - 7\) , \( a^{3} - a^{2} - 6 a + 1\) , \( -15 a^{3} - 15 a^{2} + 112 a + 160\) , \( -40 a^{3} - 51 a^{2} + 307 a + 490\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph