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	6650n	Isogeny class
Conductor	6650	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	43200	Modular degree for the optimal curve
Δ	4791990831250000 = 24 · 58 · 79 · 19	Discriminant
Eigenvalues	2+ -1 5- 7-  3  3  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-61950,4886500]	[a1,a2,a3,a4,a6]
Generators	[-240:2570:1]	Generators of the group modulo torsion
j	67312940590345/12267496528	j-invariant
L	2.6376850876177	L(r)(E,1)/r!
Ω	0.41234239435551	Real period
R	0.11845985474624	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	53200dm1 59850gl1 6650s1 46550bl1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650n1

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	-	-	3	3	2	+	-8	-2	7	-10	-1	-9	6	-6	5	-10	-14	12	12	-4	-14	-1	-9

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Quadratic twists for elliptic curve 6650n1

-4	-3	5	-7	-19
53200dm1	59850gl1	6650s1	46550bl1	126350ds1

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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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