Properties

Base field 4.4.12400.1
Label 4.4.12400.1-5.2-b
Conductor 5.2
Rank \( 1 \)

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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-b over 4.4.12400.1

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

Curve label Weierstrass Coefficients
5.2-b1 \( \bigl[1\) , \( -a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( 3\) , \( -\frac{1}{2} a^{3} - 2 a^{2} + \frac{3}{2} a + 7\bigr] \)
5.2-b2 \( \bigl[\frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{5}{2} a^{3} + 6 a^{2} + \frac{45}{2} a - 43\) , \( 7 a^{3} - \frac{19}{2} a^{2} - 62 a + \frac{211}{2}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph