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	6216i	Isogeny class
Conductor	6216	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	2349648 = 24 · 34 · 72 · 37	Discriminant
Eigenvalues	2+ 3-  2 7+ -4 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-607,5558]	[a1,a2,a3,a4,a6]
Generators	[-11:105:1]	Generators of the group modulo torsion
j	1548406847488/146853	j-invariant
L	5.0515407586244	L(r)(E,1)/r!
Ω	2.4751526029636	Real period
R	2.0409007317674	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12432f1 49728f1 18648bb1 43512d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6216i1

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

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Quadratic twists for elliptic curve 6216i1

-4	8	-3	-7
12432f1	49728f1	18648bb1	43512d1

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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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