Elliptic curves over 4.4.12400.1 of conductor 5.1

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree	Base change curves	\(\Q\)-curves	Torsion structure	CM
Analytic order* of Ш	Cyclic isogeny degree	Isogeny class size	Semistable	j-invariant
Regulator*	Curves per isogeny class	Isogeny class degree	Potential good reduction

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.

Results (4 matches)

 

Label	Base field	Conductor	Isogeny class	Weierstrass coefficients
5.1-a1	4.4.12400.1	5.1	5.1-a	\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 8\) , \( a^{3} - 2 a^{2} - 4 a + 9\bigr] \)
5.1-a2	4.4.12400.1	5.1	5.1-a	\( \bigl[\frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a + 1\) , \( \frac{3}{2} a^{3} + \frac{7}{2} a^{2} - \frac{21}{2} a - \frac{41}{2}\) , \( \frac{19}{2} a^{3} + 25 a^{2} - \frac{85}{2} a - 106\bigr] \)
5.1-b1	4.4.12400.1	5.1	5.1-b	\( \bigl[1\) , \( a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 3\) , \( -2 a^{2} + 7\bigr] \)
5.1-b2	4.4.12400.1	5.1	5.1-b	\( \bigl[\frac{1}{2} a^{2} + a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 1\) , \( \frac{1}{2} a^{2} - \frac{7}{2}\) , \( \frac{5}{2} a^{3} + \frac{11}{2} a^{2} - \frac{35}{2} a - \frac{73}{2}\) , \( -a^{3} + \frac{1}{2} a^{2} + 19 a + \frac{53}{2}\bigr] \)