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	3648v	Isogeny class
Conductor	3648	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-580977563258585088 = -1 · 223 · 312 · 194	Discriminant
Eigenvalues	2- 3+ -2  0 -4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-339969,84766113]	[a1,a2,a3,a4,a6]
j	-16576888679672833/2216253521952	j-invariant
L	0.56296835169531	L(r)(E,1)/r!
Ω	0.28148417584766	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3648r4 912k4 10944bz4 91200hm3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648v4

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 3648v4

-4	8	-3	5	-19
3648r4	912k4	10944bz4	91200hm3	69312do3

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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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