Cremona's table of elliptic curves

6650 = 2 · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 19+	Signs for the Atkin-Lehner involutions
Class	6650bf	Isogeny class
Conductor	6650	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	420000	Modular degree for the optimal curve
Δ	1955914625000000 = 26 · 59 · 77 · 19	Discriminant
Eigenvalues	2-  2 5- 7-  4 -2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-40747888,100099547281]	[a1,a2,a3,a4,a6]
j	3830972064521089212269/1001428288	j-invariant
L	5.7863121797018	L(r)(E,1)/r!
Ω	0.27553867522389	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53200do1 59850dc1 6650j1 46550dj1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650bf1

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	-	-	4	-2	6	+	4	-4	4	-10	-2	10	0	6	4	12	0	6	-14	-2	4	-6	8

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Quadratic twists for elliptic curve 6650bf1

-4	-3	5	-7	-19
53200do1	59850dc1	6650j1	46550dj1	126350bx1

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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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