Cremona's table of elliptic curves

7942 = 2 · 11 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 11- 19+	Signs for the Atkin-Lehner involutions
Class	7942f	Isogeny class
Conductor	7942	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	6480	Modular degree for the optimal curve
Δ	11101264064 = 26 · 113 · 194	Discriminant
Eigenvalues	2+ -2 -3 -1 11- -4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-730,5580]	[a1,a2,a3,a4,a6]
Generators	[-27:89:1] [-26:97:1]	Generators of the group modulo torsion
j	329474953/85184	j-invariant
L	2.6949413854199	L(r)(E,1)/r!
Ω	1.1957648226292	Real period
R	1.1268693201289	Regulator
r	2	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	63536o1 71478bt1 87362bc1 7942s1	Quadratic twists by: -4 -3 -11 -19

Hecke Eigenvalues for elliptic curve 7942f1

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
+	-2	-3	-1	-	-4	0	+	0	-6	-4	-1	-6	-4	6	3	0	-4	-4	-6	2	11	-3	-18	-19

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Quadratic twists for elliptic curve 7942f1

-4	-3	-11	-19
63536o1	71478bt1	87362bc1	7942s1

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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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