Elliptic curve isogeny class 4.2-a over number field 4.4.10025.1

• Base field: 4.4.10025.1
• Label: 4.4.10025.1-4.2-a
• Conductor: 4.2
• Rank: \( 0 \)

Base field 4.4.10025.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 10 x + 20 \); class number \(1\).

Elliptic curves in class 4.2-a over 4.4.10025.1

Isogeny class 4.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4.2-a1	\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( a^{2} - a - 6\) , \( a^{3} + 2 a^{2} - 7 a - 10\) , \( -\frac{97}{2} a^{3} - \frac{161}{2} a^{2} + \frac{619}{2} a + 352\) , \( -\frac{715}{2} a^{3} - \frac{1189}{2} a^{2} + \frac{4683}{2} a + 2675\bigr] \)
4.2-a2	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( a^{2} - 5\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - 3 a + 1\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph