Cremona's table of elliptic curves

42042 = 2 · 3 · 7² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	42042cr	Isogeny class
Conductor	42042	Conductor
∏ cp	270	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	-555325714944 = -1 · 29 · 35 · 74 · 11 · 132	Discriminant
Eigenvalues	2- 3- -1 7+ 11+ 13+  5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2206,53444]	[a1,a2,a3,a4,a6]
Generators	[-10:-268:1]	Generators of the group modulo torsion
j	-494493264769/231289344	j-invariant
L	10.23670467021	L(r)(E,1)/r!
Ω	0.86126499737193	Real period
R	0.044020970452129	Regulator
r	1	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	126126bi1 42042cd1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 42042cr1

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	+	+	+	5	-2	-3	-6	6	4	-7	-2	7	-6	-2	-1	-3	16	4	5	-5	-10	-13

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Quadratic twists for elliptic curve 42042cr1

-3	-7
126126bi1	42042cd1

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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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