Elliptic curve isogeny class 5.1-b over number field 4.4.12400.1

• Base field: 4.4.12400.1
• Label: 4.4.12400.1-5.1-b
• Conductor: 5.1
• Rank: \( 1 \)

Base field 4.4.12400.1

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

Elliptic curves in class 5.1-b over 4.4.12400.1

Isogeny class 5.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
5.1-b1	\( \bigl[1\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 3\) , \( -2 a^{2} + 7\bigr] \)
5.1-b2	\( \bigl[\frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 1\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( \frac{5}{2} a^{3} + \frac{11}{2} a^{2} - \frac{35}{2} a - \frac{73}{2}\) , \( -a^{3} + \frac{1}{2} a^{2} + 19 a + \frac{53}{2}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph