Cremona's table of elliptic curves

6216 = 2³ · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 37-	Signs for the Atkin-Lehner involutions
Class	6216t	Isogeny class
Conductor	6216	Conductor
∏ cp	448	Product of Tamagawa factors cp
Δ	-4418516861031168 = -1 · 28 · 37 · 78 · 372	Discriminant
Eigenvalues	2- 3-  0 7-  0 -6 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17948,3323376]	[a1,a2,a3,a4,a6]
Generators	[154:-2058:1]	Generators of the group modulo torsion
j	-2497791173218000/17259831488403	j-invariant
L	4.7798021580648	L(r)(E,1)/r!
Ω	0.3753276683435	Real period
R	0.11370545947511	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	12432c2 49728n2 18648n2 43512y2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6216t2

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	-	0	-6	-4	0	6	0	8	-	-6	-4	-8	-6	10	-10	4	0	6	-12	0	0	-10

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Quadratic twists for elliptic curve 6216t2

-4	8	-3	-7
12432c2	49728n2	18648n2	43512y2

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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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