Cremona's table of elliptic curves

48240 = 2⁴ · 3² · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 67+	Signs for the Atkin-Lehner involutions
Class	48240bt	Isogeny class
Conductor	48240	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	586116000000000000 = 214 · 37 · 512 · 67	Discriminant
Eigenvalues	2- 3- 5-  0  4  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-664347,205139914]	[a1,a2,a3,a4,a6]
j	10859783578981849/196289062500	j-invariant
L	3.4873797306928	L(r)(E,1)/r!
Ω	0.29061497756553	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6030y3 16080u3	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 48240bt3

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

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Quadratic twists for elliptic curve 48240bt3

-4	-3
6030y3	16080u3

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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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