Cremona's table of elliptic curves

3762 = 2 · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 19-	Signs for the Atkin-Lehner involutions
Class	3762p	Isogeny class
Conductor	3762	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	3584	Modular degree for the optimal curve
Δ	142288109568 = 214 · 37 · 11 · 192	Discriminant
Eigenvalues	2- 3-  0 -2 11- -4 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1850,-24199]	[a1,a2,a3,a4,a6]
Generators	[-23:87:1]	Generators of the group modulo torsion
j	960044289625/195182592	j-invariant
L	4.9273063450126	L(r)(E,1)/r!
Ω	0.73837511579682	Real period
R	0.47665535536822	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30096s1 120384l1 1254d1 94050bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762p1

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	-2	-	-4	-2	-	2	2	-4	2	10	-8	-2	-12	-8	-12	-12	6	-6	6	-12	6	14

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Quadratic twists for elliptic curve 3762p1

-4	8	-3	5	-11	-19
30096s1	120384l1	1254d1	94050bi1	41382n1	71478bb1

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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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