Cremona's table of elliptic curves

5618 = 2 · 53²

Field	Data	Notes
Atkin-Lehner	2+ 53+	Signs for the Atkin-Lehner involutions
Class	5618a	Isogeny class
Conductor	5618	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	324	Modular degree for the optimal curve
Δ	-22472 = -1 · 23 · 532	Discriminant
Eigenvalues	2+ -1  0  2  0 -4 -3  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5,-11]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	-6625/8	j-invariant
L	2.3870094911352	L(r)(E,1)/r!
Ω	1.4886640903211	Real period
R	1.6034574264637	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	44944a1 50562z1 5618h1	Quadratic twists by: -4 -3 53

Hecke Eigenvalues for elliptic curve 5618a1

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	0	2	0	-4	-3	4	6	0	-2	2	3	5	6	+	-12	10	-5	12	-11	16	-3	-9	-19

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Quadratic twists for elliptic curve 5618a1

-4	-3	53
44944a1	50562z1	5618h1

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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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