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	3648h	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	1.0330908321596	L(r)(E,1)/r!
Ω	0.51654541607982	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	3648l3 1824i2 10944bi3 91200dz4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648h3

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 3648h3

-4	8	-3	5	-19
3648l3	1824i2	10944bi3	91200dz4	69312bs4

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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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