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	6650g	Isogeny class
Conductor	6650	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-8493019570000000 = -1 · 27 · 57 · 73 · 195	Discriminant
Eigenvalues	2+  0 5+ 7- -1  1  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-88817,11133341]	[a1,a2,a3,a4,a6]
Generators	[229:1548:1]	Generators of the group modulo torsion
j	-4959007166945889/543553252480	j-invariant
L	2.9742446592181	L(r)(E,1)/r!
Ω	0.40222557073958	Real period
R	0.24648231204772	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	53200bk1 59850fm1 1330g1 46550f1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650g1

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

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Quadratic twists for elliptic curve 6650g1

-4	-3	5	-7	-19
53200bk1	59850fm1	1330g1	46550f1	126350ct1

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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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