Cremona's table of elliptic curves

3752 = 2³ · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 7+ 67+	Signs for the Atkin-Lehner involutions
Class	3752j	Isogeny class
Conductor	3752	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	120064 = 28 · 7 · 67	Discriminant
Eigenvalues	2- -1 -3 7+ -4 -1 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12,4]	[a1,a2,a3,a4,a6]
Generators	[-2:4:1] [0:2:1]	Generators of the group modulo torsion
j	810448/469	j-invariant
L	3.2820499069421	L(r)(E,1)/r!
Ω	2.7967141364554	Real period
R	0.29338446358898	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7504m1 30016j1 33768d1 93800k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3752j1

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
-	-1	-3	+	-4	-1	-2	-4	-3	-3	-3	-11	-9	-6	-2	-2	-4	-2	+	5	6	4	2	4	6

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Quadratic twists for elliptic curve 3752j1

-4	8	-3	5	-7
7504m1	30016j1	33768d1	93800k1	26264r1

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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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