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	6216d	Isogeny class
Conductor	6216	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	812376698112 = 28 · 36 · 76 · 37	Discriminant
Eigenvalues	2+ 3+ -2 7+  4  0  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3284,-56940]	[a1,a2,a3,a4,a6]
Generators	[-43:54:1]	Generators of the group modulo torsion
j	15304721495632/3173346477	j-invariant
L	2.9290965871311	L(r)(E,1)/r!
Ω	0.63985871334625	Real period
R	2.2888619987785	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	12432s2 49728bx2 18648y2 43512k2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6216d2

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

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Quadratic twists for elliptic curve 6216d2

-4	8	-3	-7
12432s2	49728bx2	18648y2	43512k2

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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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