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	3648bb	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]
Generators	[4:3:1]	Generators of the group modulo torsion
j	8192/171	j-invariant
L	3.4652564956614	L(r)(E,1)/r!
Ω	1.2378152840168	Real period
R	1.3997470141168	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3648m1 912i1 10944cp1 91200ia1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648bb1

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 3648bb1

-4	8	-3	5	-19
3648m1	912i1	10944cp1	91200ia1	69312ds1

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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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