Elliptic curve isogeny class 5.2-a over number field 4.4.12400.1

• Base field: 4.4.12400.1
• Label: 4.4.12400.1-5.2-a
• Conductor: 5.2
• Rank: \( 0 \)

Base field 4.4.12400.1

Generator \(a\), with minimal polynomial \( x^{4} - 12 x^{2} + 31 \); class number \(1\).

Elliptic curves in class 5.2-a over 4.4.12400.1

Isogeny class 5.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
5.2-a1	\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 8\) , \( -\frac{3}{2} a^{3} - 2 a^{2} + \frac{13}{2} a + 9\bigr] \)
5.2-a2	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( -\frac{13}{2} a^{3} + 14 a^{2} + \frac{107}{2} a - 112\) , \( -\frac{91}{2} a^{3} + 89 a^{2} + \frac{747}{2} a - 728\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph