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	6650r	Isogeny class
Conductor	6650	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-195562950625000 = -1 · 23 · 57 · 74 · 194	Discriminant
Eigenvalues	2-  0 5+ 7+  4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3880,-678253]	[a1,a2,a3,a4,a6]
j	-413327139849/12516028840	j-invariant
L	2.9518939149554	L(r)(E,1)/r!
Ω	0.24599115957961	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	53200cp3 59850bg3 1330c4 46550cg3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650r4

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

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Quadratic twists for elliptic curve 6650r4

-4	-3	5	-7	-19
53200cp3	59850bg3	1330c4	46550cg3	126350k3

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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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