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	6	Product of Tamagawa factors cp
Δ	375791550464 = 218 · 11 · 194	Discriminant
Eigenvalues	2+ -2 -3 -1 11- -4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-20585,-1138068]	[a1,a2,a3,a4,a6]
Generators	[-84:51:1] [315:4706:1]	Generators of the group modulo torsion
j	7401701968633/2883584	j-invariant
L	2.6949413854199	L(r)(E,1)/r!
Ω	0.39858827420972	Real period
R	1.1268693201289	Regulator
r	2	Rank of the group of rational points
S	0.99999999999983	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63536o2 71478bt2 87362bc2 7942s2	Quadratic twists by: -4 -3 -11 -19

Hecke Eigenvalues for elliptic curve 7942f2

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 7942f2

-4	-3	-11	-19
63536o2	71478bt2	87362bc2	7942s2

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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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