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	16	Product of Tamagawa factors cp
Δ	851705856 = 218 · 32 · 192	Discriminant
Eigenvalues	2- 3-  2  0  0 -6 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-417,-3105]	[a1,a2,a3,a4,a6]
Generators	[498:11115:1]	Generators of the group modulo torsion
j	30664297/3249	j-invariant
L	4.4803486366504	L(r)(E,1)/r!
Ω	1.0635210982656	Real period
R	4.2127501221714	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	3648g2 912g2 10944cb2 91200ez2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648bf2

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 3648bf2

-4	8	-3	5	-19
3648g2	912g2	10944cb2	91200ez2	69312cp2

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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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