Cremona's table of elliptic curves

53200 = 2⁴ · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	53200co	Isogeny class
Conductor	53200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	222720	Modular degree for the optimal curve
Δ	-808640000000 = -1 · 212 · 57 · 7 · 192	Discriminant
Eigenvalues	2-  3 5+ 7-  3 -3 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-38800,2942000]	[a1,a2,a3,a4,a6]
Generators	[2235:14725:27]	Generators of the group modulo torsion
j	-100934332416/12635	j-invariant
L	11.798026642679	L(r)(E,1)/r!
Ω	0.86046033658884	Real period
R	3.4278240788445	Regulator
r	1	Rank of the group of rational points
S	1.0000000000067	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3325f1 10640w1	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 53200co1

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	+	-	3	-3	-3	+	-4	1	-8	4	-8	-4	1	12	-6	-6	4	0	-10	-13	4	-6	-5

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Quadratic twists for elliptic curve 53200co1

-4	5
3325f1	10640w1

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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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