Elliptic curve isogeny class 20.1-c over number field 4.4.18625.1

• Base field: 4.4.18625.1
• Label: 4.4.18625.1-20.1-c
• Conductor: 20.1
• Rank: \( 1 \)

Base field 4.4.18625.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 14 x^{2} + 9 x + 41 \); class number \(1\).

Elliptic curves in class 20.1-c over 4.4.18625.1

Isogeny class 20.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.1-c1	\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( 0\) , \( \frac{43}{6} a^{3} - 16 a^{2} - \frac{40}{3} a + \frac{133}{6}\) , \( -\frac{55}{2} a^{3} + 136 a^{2} + 5 a - \frac{855}{2}\bigr] \)
20.1-c2	\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{35}{6}\) , \( 33 a^{3} - 9 a^{2} - 298 a + 137\) , \( \frac{675}{2} a^{3} - 575 a^{2} - 3184 a + \frac{11145}{2}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph