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	5200g	Isogeny class
Conductor	5200	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	14060800 = 28 · 52 · 133	Discriminant
Eigenvalues	2+  3 5+  2  2 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-100,-340]	[a1,a2,a3,a4,a6]
j	17280000/2197	j-invariant
L	4.5670756902224	L(r)(E,1)/r!
Ω	1.5223585634075	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	2600k1 20800ct1 46800be1 5200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200g1

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
+	3	+	2	2	-	-2	-4	1	1	2	0	12	-5	4	9	-8	7	14	0	6	15	-4	-18	-16

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Quadratic twists for elliptic curve 5200g1

-4	8	-3	5	13
2600k1	20800ct1	46800be1	5200i1	67600r1

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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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