Elliptic curve isogeny class 20.1-b over number field 4.4.6809.1

• Base field: 4.4.6809.1
• Label: 4.4.6809.1-20.1-b
• Conductor: 20.1
• Rank: \( 1 \)

Base field 4.4.6809.1

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

Elliptic curves in class 20.1-b over 4.4.6809.1

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

Curve label	Weierstrass Coefficients
20.1-b1	\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 12 a^{3} - 9 a^{2} - 31 a - 13\) , \( 45 a^{3} - 50 a^{2} - 101 a - 33\bigr] \)
20.1-b2	\( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 2 a^{3} + a^{2} - 6 a - 3\) , \( 2 a^{3} - 4 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph