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	6650m	Isogeny class
Conductor	6650	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-16625000000 = -1 · 26 · 59 · 7 · 19	Discriminant
Eigenvalues	2+ -1 5- 7- -2 -2 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,550,-3500]	[a1,a2,a3,a4,a6]
Generators	[60:470:1]	Generators of the group modulo torsion
j	9393931/8512	j-invariant
L	2.2934565725541	L(r)(E,1)/r!
Ω	0.67774081672166	Real period
R	0.84599323073379	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	53200dk1 59850gi1 6650bc1 46550bk1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650m1

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	-2	-3	+	7	8	-8	5	-11	1	6	9	10	0	6	-3	7	16	-14	-6	-4

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Quadratic twists for elliptic curve 6650m1

-4	-3	5	-7	-19
53200dk1	59850gi1	6650bc1	46550bk1	126350dr1

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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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