Cremona's table of elliptic curves

4655 = 5 · 7² · 19

Field	Data	Notes
Atkin-Lehner	5+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	4655h	Isogeny class
Conductor	4655	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11136	Modular degree for the optimal curve
Δ	-1486495115 = -1 · 5 · 77 · 192	Discriminant
Eigenvalues	-2 -3 5+ 7- -3 -3 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-4753,126138]	[a1,a2,a3,a4,a6]
Generators	[-56:465:1] [-21:465:1]	Generators of the group modulo torsion
j	-100934332416/12635	j-invariant
L	1.6325963669817	L(r)(E,1)/r!
Ω	1.4544434289864	Real period
R	0.14031109206845	Regulator
r	2	Rank of the group of rational points
S	0.9999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74480bv1 41895bm1 23275q1 665e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4655h1

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	-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 4655h1

-4	-3	5	-7	-19
74480bv1	41895bm1	23275q1	665e1	88445x1

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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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