Cremona's table of elliptic curves

3648 = 2⁶ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	3648bf	Isogeny class
Conductor	3648	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-102488604672 = -1 · 218 · 3 · 194	Discriminant
Eigenvalues	2- 3-  2  0  0 -6 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,543,-14433]	[a1,a2,a3,a4,a6]
Generators	[1093274:24437895:2197]	Generators of the group modulo torsion
j	67419143/390963	j-invariant
L	4.4803486366504	L(r)(E,1)/r!
Ω	0.53176054913282	Real period
R	8.4255002443428	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	3648g4 912g4 10944cb4 91200ez3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648bf4

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	0	0	-6	-6	+	-4	-2	-8	10	-2	-4	-12	6	-12	2	-4	0	10	0	16	-2	10

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Quadratic twists for elliptic curve 3648bf4

-4	8	-3	5	-19
3648g4	912g4	10944cb4	91200ez3	69312cp3

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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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