Elliptic curve isogeny class 20.2-a over number field 4.4.18625.1

• Base field: 4.4.18625.1
• Label: 4.4.18625.1-20.2-a
• Conductor: 20.2
• 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 20.2-a over 4.4.18625.1

Isogeny class 20.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.2-a1	\( \bigl[a\) , \( -a^{2} + a + 8\) , \( a\) , \( -\frac{5}{6} a^{3} - a^{2} + \frac{17}{3} a + \frac{79}{6}\) , \( \frac{145}{6} a^{3} - 104 a^{2} - \frac{85}{3} a + \frac{2077}{6}\bigr] \)
20.2-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -\frac{19}{3} a^{3} + 21 a^{2} + \frac{179}{3} a - \frac{592}{3}\) , \( \frac{89}{2} a^{3} - 83 a^{2} - 436 a + \frac{1507}{2}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph