Cremona's table of elliptic curves

3872 = 2⁵ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	3872j	Isogeny class
Conductor	3872	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-79819452416 = -1 · 212 · 117	Discriminant
Eigenvalues	2- -1  1  4 11-  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5485,-155131]	[a1,a2,a3,a4,a6]
Generators	[235:3388:1]	Generators of the group modulo torsion
j	-2515456/11	j-invariant
L	3.5241480546815	L(r)(E,1)/r!
Ω	0.27730338301936	Real period
R	1.5885796344736	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3872i1 7744w1 34848r1 96800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3872j1

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	1	4	-	2	0	-2	-9	-4	-5	-9	-2	-6	4	-6	5	0	13	1	-14	-10	14	-13	-19

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Quadratic twists for elliptic curve 3872j1

-4	8	-3	5	-11
3872i1	7744w1	34848r1	96800j1	352c1

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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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