Cremona's table of elliptic curves

3872 = 2⁵ · 11²

Field	Data	Notes
Atkin-Lehner	2+ 11-	Signs for the Atkin-Lehner involutions
Class	3872d	Isogeny class
Conductor	3872	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	-878013976576 = -1 · 212 · 118	Discriminant
Eigenvalues	2+  2  1  2 11-  1  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1775,34113]	[a1,a2,a3,a4,a6]
j	704	j-invariant
L	3.6046664103908	L(r)(E,1)/r!
Ω	0.60077773506513	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3872e1 7744be1 34848bx1 96800cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3872d1

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 3872d1

-4	8	-3	5	-11
3872e1	7744be1	34848bx1	96800cb1	3872l1

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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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