Cremona's table of elliptic curves

6270 = 2 · 3 · 5 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	6270c	Isogeny class
Conductor	6270	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	18810000 = 24 · 32 · 54 · 11 · 19	Discriminant
Eigenvalues	2+ 3+ 5-  0 11+ -6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-72,-144]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	42180533641/18810000	j-invariant
L	2.5078222137816	L(r)(E,1)/r!
Ω	1.7052753331587	Real period
R	0.36765649584814	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50160cg1 18810y1 31350bw1 68970bt1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6270c1

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

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Quadratic twists for elliptic curve 6270c1

-4	-3	5	-11	-19
50160cg1	18810y1	31350bw1	68970bt1	119130bs1

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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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