Cremona's table of elliptic curves

3948 = 2² · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 47+	Signs for the Atkin-Lehner involutions
Class	3948d	Isogeny class
Conductor	3948	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	8160	Modular degree for the optimal curve
Δ	-1232958757632 = -1 · 28 · 3 · 7 · 475	Discriminant
Eigenvalues	2- 3-  0 7- -1  2 -5  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-29373,1928607]	[a1,a2,a3,a4,a6]
j	-10948218293248000/4816245147	j-invariant
L	2.5485539729276	L(r)(E,1)/r!
Ω	0.84951799097588	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15792o1 63168p1 11844f1 98700e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3948d1

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	-	-1	2	-5	1	9	6	-7	7	2	6	+	14	-5	10	-2	6	-15	1	3	7	-10

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Quadratic twists for elliptic curve 3948d1

-4	8	-3	5	-7
15792o1	63168p1	11844f1	98700e1	27636g1

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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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