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	3648l	Isogeny class
Conductor	3648	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	5603328 = 215 · 32 · 19	Discriminant
Eigenvalues	2+ 3-  2  4  4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7297,237503]	[a1,a2,a3,a4,a6]
j	1311494070536/171	j-invariant
L	3.7423198595715	L(r)(E,1)/r!
Ω	1.8711599297858	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3648h3 1824c3 10944s3 91200n4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648l3

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

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Quadratic twists for elliptic curve 3648l3

-4	8	-3	5	-19
3648h3	1824c3	10944s3	91200n4	69312q4

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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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