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	6650bi	Isogeny class
Conductor	6650	Conductor
∏ cp	500	Product of Tamagawa factors cp
Δ	-5326821874304000 = -1 · 210 · 53 · 75 · 195	Discriminant
Eigenvalues	2- -1 5- 7-  2 -6  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-15953,-3602769]	[a1,a2,a3,a4,a6]
Generators	[295:4032:1]	Generators of the group modulo torsion
j	-3592051016566949/42614574994432	j-invariant
L	5.0781125328579	L(r)(E,1)/r!
Ω	0.18303741707287	Real period
R	1.3871788113236	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	53200cz2 59850dk2 6650l2 46550ct2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650bi2

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	-	-	2	-6	3	-	-1	0	-8	3	-3	9	-2	-1	-10	-8	-2	-13	9	0	-6	10	-12

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Quadratic twists for elliptic curve 6650bi2

-4	-3	5	-7	-19
53200cz2	59850dk2	6650l2	46550ct2	126350bt2

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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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