Cremona's table of elliptic curves

3870 = 2 · 3² · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 43+	Signs for the Atkin-Lehner involutions
Class	3870n	Isogeny class
Conductor	3870	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	9984600000000 = 29 · 33 · 58 · 432	Discriminant
Eigenvalues	2- 3+ 5- -2 -2  2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-9872,348019]	[a1,a2,a3,a4,a6]
Generators	[-23:761:1]	Generators of the group modulo torsion
j	3940344055317123/369800000000	j-invariant
L	5.2018689215331	L(r)(E,1)/r!
Ω	0.70548331896998	Real period
R	0.10240947946327	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30960z2 123840k2 3870a2 19350f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3870n2

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	-2	2	0	-8	-8	2	0	-8	-8	+	0	2	6	8	12	0	-2	-12	-18	6	-2

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Quadratic twists for elliptic curve 3870n2

-4	8	-3	5
30960z2	123840k2	3870a2	19350f2

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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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