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	3762a	Isogeny class
Conductor	3762	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	18720	Modular degree for the optimal curve
Δ	-493398997622784 = -1 · 213 · 39 · 115 · 19	Discriminant
Eigenvalues	2+ 3+  3  0 11+ -4 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4443,1075877]	[a1,a2,a3,a4,a6]
Generators	[-83:973:1]	Generators of the group modulo torsion
j	-492851793699/25067266048	j-invariant
L	3.0834928004466	L(r)(E,1)/r!
Ω	0.43407236237174	Real period
R	3.5518188529657	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30096r1 120384j1 3762m1 94050ch1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762a1

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
+	+	3	0	+	-4	-5	+	2	-3	8	-3	2	-11	-6	8	10	-15	-15	-4	6	-16	6	3	-10

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Quadratic twists for elliptic curve 3762a1

-4	8	-3	5	-11	-19
30096r1	120384j1	3762m1	94050ch1	41382bn1	71478bk1

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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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