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	1000	Product of Tamagawa factors cp
deg	32000	Modular degree for the optimal curve
Δ	-434411683200000 = -1 · 210 · 310 · 55 · 112 · 19	Discriminant
Eigenvalues	2- 3- 5- -2 11- -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-27275,2000625]	[a1,a2,a3,a4,a6]
Generators	[-150:1725:1]	Generators of the group modulo torsion
j	-2243980016705847601/434411683200000	j-invariant
L	6.8740037014054	L(r)(E,1)/r!
Ω	0.50782646680533	Real period
R	1.3536127300826	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	50160bl1 18810d1 31350f1 68970bh1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6270r1

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 6270r1

-4	-3	5	-11	-19
50160bl1	18810d1	31350f1	68970bh1	119130k1

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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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