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	3648r	Isogeny class
Conductor	3648	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	4303355904 = 223 · 33 · 19	Discriminant
Eigenvalues	2+ 3- -2  0  4 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5603329,-5107121569]	[a1,a2,a3,a4,a6]
Generators	[7918918:144304215:2744]	Generators of the group modulo torsion
j	74220219816682217473/16416	j-invariant
L	3.797823553099	L(r)(E,1)/r!
Ω	0.098126886118786	Real period
R	12.901063454045	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	3648v3 114c3 10944bg3 91200v4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648r3

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

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Quadratic twists for elliptic curve 3648r3

-4	8	-3	5	-19
3648v3	114c3	10944bg3	91200v4	69312t4

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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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