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	6270r	Isogeny class
Conductor	6270	Conductor
∏ cp	500	Product of Tamagawa factors cp
Δ	301547812500000 = 25 · 35 · 510 · 11 · 192	Discriminant
Eigenvalues	2- 3- 5- -2 11- -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-454955,118072977]	[a1,a2,a3,a4,a6]
Generators	[-776:2383:1]	Generators of the group modulo torsion
j	10414276373665867414321/301547812500000	j-invariant
L	6.8740037014054	L(r)(E,1)/r!
Ω	0.50782646680533	Real period
R	2.7072254601651	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	10	Number of elements in the torsion subgroup
Twists	50160bl2 18810d2 31350f2 68970bh2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6270r2

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	-	-6	-2	+	-6	0	-8	-2	2	4	-2	-6	0	2	-12	2	4	-10	14	0	-2

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Quadratic twists for elliptic curve 6270r2

-4	-3	5	-11	-19
50160bl2	18810d2	31350f2	68970bh2	119130k2

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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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