Cremona's table of elliptic curves

4136 = 2³ · 11 · 47

Field	Data	Notes
Atkin-Lehner	2- 11+ 47-	Signs for the Atkin-Lehner involutions
Class	4136d	Isogeny class
Conductor	4136	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-6220544 = -1 · 28 · 11 · 472	Discriminant
Eigenvalues	2-  1  3  0 11+ -6 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-49,163]	[a1,a2,a3,a4,a6]
Generators	[21:94:1]	Generators of the group modulo torsion
j	-51868672/24299	j-invariant
L	4.7009418148356	L(r)(E,1)/r!
Ω	2.2267648470486	Real period
R	0.52777708219464	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	8272d1 33088q1 37224g1 103400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4136d1

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	3	0	+	-6	-2	-2	-9	8	7	-1	0	0	-	-6	-5	-8	-11	-5	4	-8	8	-17	13

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Quadratic twists for elliptic curve 4136d1

-4	8	-3	5	-11
8272d1	33088q1	37224g1	103400b1	45496b1

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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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