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	3870m	Isogeny class
Conductor	3870	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	248846777786934000 = 24 · 39 · 53 · 436	Discriminant
Eigenvalues	2- 3+ 5+ -4  0  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-332723,69946147]	[a1,a2,a3,a4,a6]
Generators	[685:12428:1]	Generators of the group modulo torsion
j	206956783279200843/12642726098000	j-invariant
L	4.6039644387046	L(r)(E,1)/r!
Ω	0.30665287837344	Real period
R	1.2511335463747	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	30960s4 123840u4 3870d2 19350c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3870m4

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
-	+	+	-4	0	2	6	2	-6	-6	-4	-4	0	-	-6	6	-12	-10	-4	0	-4	-4	6	6	-10

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Quadratic twists for elliptic curve 3870m4

-4	8	-3	5
30960s4	123840u4	3870d2	19350c4

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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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