Cremona's table of elliptic curves

4650 = 2 · 3 · 5² · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	4650bp	Isogeny class
Conductor	4650	Conductor
∏ cp	150	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	-1499561164800 = -1 · 215 · 310 · 52 · 31	Discriminant
Eigenvalues	2- 3- 5+  3 -3 -1 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1428,62352]	[a1,a2,a3,a4,a6]
j	-12882119799145/59982446592	j-invariant
L	4.4262201292027	L(r)(E,1)/r!
Ω	0.73770335486712	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	37200bo1 13950ba1 4650m2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 4650bp1

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	-1	-2	0	4	10	-	3	7	-1	-7	9	0	7	-2	7	4	-10	9	10	-2

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Quadratic twists for elliptic curve 4650bp1

-4	-3	5
37200bo1	13950ba1	4650m2

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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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