Elliptic curve isogeny class 20.1-c over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-20.1-c
• Conductor: 20.1
• Rank: \( 0 \)

Base field 4.4.5744.1

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

Elliptic curves in class 20.1-c over 4.4.5744.1

Isogeny class 20.1-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
20.1-c1	\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -a^{2} + 2 a + 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 5 a^{3} - 22 a - 13\) , \( -3 a^{3} - 2 a^{2} + 17 a + 12\bigr] \)
20.1-c2	\( \bigl[-a^{3} + a^{2} + 4 a\) , \( -a^{2} + 2 a + 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 190 a^{3} - 575 a^{2} + 223 a + 157\) , \( 6830 a^{3} - 13997 a^{2} - 6416 a + 2462\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph