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	6650bb	Isogeny class
Conductor	6650	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	1361920000 = 214 · 54 · 7 · 19	Discriminant
Eigenvalues	2-  1 5- 7+  1 -3  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-538,-4508]	[a1,a2,a3,a4,a6]
Generators	[-12:22:1]	Generators of the group modulo torsion
j	27557573425/2179072	j-invariant
L	6.6841597383736	L(r)(E,1)/r!
Ω	0.99625820896432	Real period
R	0.47923317169827	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	53200dz1 59850co1 6650e1 46550de1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650bb1

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	-	+	1	-3	2	+	4	-8	-1	-4	-5	-11	-2	-10	-13	8	8	4	10	2	0	15	-13

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Quadratic twists for elliptic curve 6650bb1

-4	-3	5	-7	-19
53200dz1	59850co1	6650e1	46550de1	126350bf1

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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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