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	5200w	Isogeny class
Conductor	5200	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	38020403200 = 212 · 52 · 135	Discriminant
Eigenvalues	2-  1 5+  2 -2 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1573,-22637]	[a1,a2,a3,a4,a6]
Generators	[-18:13:1]	Generators of the group modulo torsion
j	4206161920/371293	j-invariant
L	4.5718121794283	L(r)(E,1)/r!
Ω	0.76231612512862	Real period
R	1.199453095304	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	325e1 20800ck1 46800dw1 5200bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200w1

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	+	2	-2	-	-2	0	-9	5	-2	8	12	1	-8	-11	0	-13	2	-12	-6	-15	-4	-10	8

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Quadratic twists for elliptic curve 5200w1

-4	8	-3	5	13
325e1	20800ck1	46800dw1	5200bf2	67600bq1

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

Part of Computational Number Theory
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