Cremona's table of elliptic curves

5200 = 2⁴ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	5200c	Isogeny class
Conductor	5200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-332800 = -1 · 210 · 52 · 13	Discriminant
Eigenvalues	2+  2 5+  3 -3 13+ -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,32]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	-2500/13	j-invariant
L	5.453070647225	L(r)(E,1)/r!
Ω	2.63695212343	Real period
R	1.0339722512921	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2600b1 20800dh1 46800t1 5200m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	2	+	3	-3	+	-3	-4	-6	1	-3	-10	-8	-10	1	1	7	7	11	0	-6	0	-1	2	16

---

Quadratic twists for elliptic curve 5200c1

-4	8	-3	5	13
2600b1	20800dh1	46800t1	5200m1	67600p1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations