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	3648m	Isogeny class
Conductor	3648	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-2801664 = -1 · 214 · 32 · 19	Discriminant
Eigenvalues	2+ 3-  3  1  5  6 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,11,83]	[a1,a2,a3,a4,a6]
j	8192/171	j-invariant
L	3.8114529238654	L(r)(E,1)/r!
Ω	1.9057264619327	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3648bb1 228b1 10944v1 91200b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648m1

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
+	-	3	1	5	6	-5	+	4	-6	6	8	-8	-9	1	-2	8	-11	0	-4	-11	-8	4	10	-10

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Quadratic twists for elliptic curve 3648m1

-4	8	-3	5	-19
3648bb1	228b1	10944v1	91200b1	69312v1

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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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