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	3762g	Isogeny class
Conductor	3762	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	9408	Modular degree for the optimal curve
Δ	-15397129731456 = -1 · 27 · 313 · 11 · 193	Discriminant
Eigenvalues	2+ 3-  1  2 11-  0 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-29484,1965136]	[a1,a2,a3,a4,a6]
Generators	[95:74:1]	Generators of the group modulo torsion
j	-3888335020909249/21120891264	j-invariant
L	3.0013614130697	L(r)(E,1)/r!
Ω	0.70298149952478	Real period
R	1.0673685634325	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	30096ba1 120384y1 1254f1 94050dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762g1

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	2	-	0	-5	+	-4	-3	6	-3	-6	1	-12	-14	0	-5	-5	0	0	8	2	5	4

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Quadratic twists for elliptic curve 3762g1

-4	8	-3	5	-11	-19
30096ba1	120384y1	1254f1	94050dc1	41382cg1	71478cn1

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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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