Elliptic curve isogeny class 20.1-b over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-20.1-b
• 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-b over 4.4.5744.1

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

Curve label	Weierstrass Coefficients
20.1-b1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -142 a^{3} - 40 a^{2} + 465 a - 52\) , \( -214 a^{3} + 1549 a^{2} + 3424 a - 945\bigr] \)
20.1-b2	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3 a^{3} - 15 a - 7\) , \( 2 a^{3} + a^{2} - 10 a - 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph