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	3762m	Isogeny class
Conductor	3762	Conductor
∏ cp	130	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	-676816183296 = -1 · 213 · 33 · 115 · 19	Discriminant
Eigenvalues	2- 3+ -3  0 11- -4  5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-494,-39683]	[a1,a2,a3,a4,a6]
Generators	[85:683:1]	Generators of the group modulo torsion
j	-492851793699/25067266048	j-invariant
L	4.4345590350623	L(r)(E,1)/r!
Ω	0.39787309881166	Real period
R	0.08573586070354	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	30096n1 120384e1 3762a1 94050d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762m1

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 3762m1

-4	8	-3	5	-11	-19
30096n1	120384e1	3762a1	94050d1	41382g1	71478g1

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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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