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	5200q	Isogeny class
Conductor	5200	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	1331200 = 212 · 52 · 13	Discriminant
Eigenvalues	2-  1 5+ -4  6 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-53,-157]	[a1,a2,a3,a4,a6]
j	163840/13	j-invariant
L	1.7755377143316	L(r)(E,1)/r!
Ω	1.7755377143316	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	325b1 20800dc1 46800dn1 5200bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200q1

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
-	1	+	-4	6	+	-6	4	3	-3	4	-2	6	-7	0	9	6	-1	14	6	4	-11	-6	0	10

---

Quadratic twists for elliptic curve 5200q1

-4	8	-3	5	13
325b1	20800dc1	46800dn1	5200bh1	67600bs1

---

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