Cremona's table of elliptic curves

3872 = 2⁵ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	3872m	Isogeny class
Conductor	3872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-495616 = -1 · 212 · 112	Discriminant
Eigenvalues	2- -2  1  2 11- -1 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,15,31]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	704	j-invariant
L	2.8489614895361	L(r)(E,1)/r!
Ω	1.9925543296106	Real period
R	0.35745091704638	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	3872l1 7744ba1 34848p1 96800r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3872m1

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	1	2	-	-1	-3	2	6	-1	-10	-3	-11	12	-10	9	4	-6	2	8	10	-2	-14	-1	11

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Quadratic twists for elliptic curve 3872m1

-4	8	-3	5	-11
3872l1	7744ba1	34848p1	96800r1	3872e1

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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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