Cremona's table of elliptic curves

5618 = 2 · 53²

Field	Data	Notes
Atkin-Lehner	2- 53-	Signs for the Atkin-Lehner involutions
Class	5618i	Isogeny class
Conductor	5618	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	-152450048 = -1 · 210 · 533	Discriminant
Eigenvalues	2-  1 -2  2 -2 -1 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2364,44048]	[a1,a2,a3,a4,a6]
Generators	[22:42:1]	Generators of the group modulo torsion
j	-9814089221/1024	j-invariant
L	6.0606408218453	L(r)(E,1)/r!
Ω	1.7517566869971	Real period
R	0.17298751781089	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	44944k2 50562r2 5618d2	Quadratic twists by: -4 -3 53

Hecke Eigenvalues for elliptic curve 5618i2

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	-1	-3	-1	9	-5	0	7	0	6	-12	-	0	-10	-8	-5	-14	-11	-9	10	-7

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Quadratic twists for elliptic curve 5618i2

-4	-3	53
44944k2	50562r2	5618d2

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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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