Elliptic curve isogeny class 20.1-a over number field 4.4.6809.1

• Base field: 4.4.6809.1
• Label: 4.4.6809.1-20.1-a
• Conductor: 20.1
• Rank: \( 0 \)

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-a over 4.4.6809.1

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

Curve label	Weierstrass Coefficients
20.1-a1	\( \bigl[a^{2} - 3\) , \( a^{3} - 4 a - 1\) , \( 0\) , \( 8 a^{3} + 24 a^{2} + 12 a - 8\) , \( 25 a^{3} + 75 a^{2} + 36 a - 24\bigr] \)
20.1-a2	\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 4\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -2 a^{3} + 8 a + 2\) , \( -3 a^{3} + a^{2} + 14 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph