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	6650w	Isogeny class
Conductor	6650	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-750203125000 = -1 · 23 · 59 · 7 · 193	Discriminant
Eigenvalues	2-  2 5+ 7+ -3 -5  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,787,-40469]	[a1,a2,a3,a4,a6]
Generators	[125:1362:1]	Generators of the group modulo torsion
j	3449795831/48013000	j-invariant
L	7.6431898989014	L(r)(E,1)/r!
Ω	0.44048386129136	Real period
R	0.96398914549382	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	53200cl2 59850bm2 1330e2 46550ce2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6650w2

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
-	2	+	+	-3	-5	3	-	-3	-3	-4	-8	-3	4	-6	0	-9	5	7	-3	-2	-13	9	-6	-2

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Quadratic twists for elliptic curve 6650w2

-4	-3	5	-7	-19
53200cl2	59850bm2	1330e2	46550ce2	126350s2

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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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