Cremona's table of elliptic curves

3936 = 2⁵ · 3 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 41-	Signs for the Atkin-Lehner involutions
Class	3936d	Isogeny class
Conductor	3936	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	705858624 = 26 · 38 · 412	Discriminant
Eigenvalues	2- 3+ -2  4 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2214,40824]	[a1,a2,a3,a4,a6]
Generators	[-22:280:1]	Generators of the group modulo torsion
j	18761723501248/11029041	j-invariant
L	2.9449574236784	L(r)(E,1)/r!
Ω	1.5891539947646	Real period
R	3.706321015308	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3936f1 7872bh2 11808g1 98400bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3936d1

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	4	-4	-2	2	4	0	-2	0	-2	-	-8	-4	6	0	6	4	-12	10	4	0	-6	2

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Quadratic twists for elliptic curve 3936d1

-4	8	-3	5
3936f1	7872bh2	11808g1	98400bi1

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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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