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	5200bi	Isogeny class
Conductor	5200	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-359956480000 = -1 · 218 · 54 · 133	Discriminant
Eigenvalues	2-  2 5-  1 -3 13-  3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1592,-15888]	[a1,a2,a3,a4,a6]
j	174196775/140608	j-invariant
L	3.1828156116418	L(r)(E,1)/r!
Ω	0.53046926860697	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	650g2 20800du2 46800ff2 5200r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200bi2

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	-	1	-3	-	3	4	6	-3	1	2	0	10	3	3	15	-13	13	0	-10	4	-15	6	-4

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Quadratic twists for elliptic curve 5200bi2

-4	8	-3	5	13
650g2	20800du2	46800ff2	5200r2	67600dc2

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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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