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	7942r	Isogeny class
Conductor	7942	Conductor
∏ cp	81	Product of Tamagawa factors cp
deg	73872	Modular degree for the optimal curve
Δ	-11573822672676352 = -1 · 29 · 113 · 198	Discriminant
Eigenvalues	2- -2  0  2 11- -1 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-187908,-31792112]	[a1,a2,a3,a4,a6]
Generators	[1632:62500:1]	Generators of the group modulo torsion
j	-43204686625/681472	j-invariant
L	4.6965229474501	L(r)(E,1)/r!
Ω	0.11454503316001	Real period
R	4.555726849553	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	63536n1 71478h1 87362h1 7942j1	Quadratic twists by: -4 -3 -11 -19

Hecke Eigenvalues for elliptic curve 7942r1

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	0	2	-	-1	-6	+	0	9	8	-10	-6	5	-3	-6	6	-13	-10	9	-4	8	-9	15	-1

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Quadratic twists for elliptic curve 7942r1

-4	-3	-11	-19
63536n1	71478h1	87362h1	7942j1

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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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