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	5200s	Isogeny class
Conductor	5200	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2879651840000000 = 224 · 57 · 133	Discriminant
Eigenvalues	2- -2 5+ -4  6 13+  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-83008,8807988]	[a1,a2,a3,a4,a6]
j	988345570681/44994560	j-invariant
L	0.89444373547214	L(r)(E,1)/r!
Ω	0.44722186773607	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	650j3 20800de3 46800do3 1040g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200s3

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	+	-4	6	+	6	-2	6	-6	-2	-2	-6	2	-12	-6	-6	2	-4	6	10	4	0	-6	-2

---

Quadratic twists for elliptic curve 5200s3

-4	8	-3	5	13
650j3	20800de3	46800do3	1040g3	67600cf3

---

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