Cremona's table of elliptic curves

3872 = 2⁵ · 11²

Field	Data	Notes
Atkin-Lehner	2+ 11+	Signs for the Atkin-Lehner involutions
Class	3872a	Isogeny class
Conductor	3872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2640	Modular degree for the optimal curve
Δ	-150908652224 = -1 · 26 · 119	Discriminant
Eigenvalues	2+  0  2  0 11+  4 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1331,0]	[a1,a2,a3,a4,a6]
Generators	[1875:17650:27]	Generators of the group modulo torsion
j	1728	j-invariant
L	3.9054589343342	L(r)(E,1)/r!
Ω	0.61392130384236	Real period
R	6.3614976543264	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	3872a1 7744p2 34848br1 96800bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3872a1

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
+	0	2	0	+	4	-8	0	0	-4	0	-2	-8	0	0	14	0	-12	0	0	-16	0	0	10	-18

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Quadratic twists for elliptic curve 3872a1

-4	8	-3	5	-11
3872a1	7744p2	34848br1	96800bi1	3872h1

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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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